{"id":122194,"date":"2022-03-25T18:08:22","date_gmt":"2022-03-25T12:38:22","guid":{"rendered":"https:\/\/www.aakash.ac.in\/blog\/?post_type=web-story&#038;p=122194"},"modified":"2022-08-11T23:45:59","modified_gmt":"2022-08-11T18:15:59","slug":"maths-concept-note-from-ncert-properties-of-determinants","status":"publish","type":"web-story","link":"https:\/\/www.aakash.ac.in\/blog\/web-stories\/maths-concept-note-from-ncert-properties-of-determinants\/","title":{"rendered":"Maths Concept Note from NCERT: Properties of Determinants"},"content":{"rendered":"<p><html amp=\"\" lang=\"en\"><head><meta charSet=\"utf-8\"\/><meta name=\"viewport\" content=\"width=device-width,minimum-scale=1,initial-scale=1\"\/><script async=\"\" src=\"https:\/\/cdn.ampproject.org\/v0.js\"><\/script><script async=\"\" src=\"https:\/\/cdn.ampproject.org\/v0\/amp-story-1.0.js\" custom-element=\"amp-story\"><\/script><link 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standalone=\"\" publisher=\"Aakash BYJU&amp;#039;S Blog\" publisher-logo-src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/08\/blue.png\" title=\"Maths Concept Note from NCERT: Properties of Determinants\" poster-portrait-src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/cropped-determinants-properties1.jpg\"><amp-story-page id=\"568b5f37-c29f-440f-8679-4637776b9f67\" auto-advance-after=\"7s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-ca1796c5-579e-4474-aeab-1aa45d2428f6\",\"keyframes\":{\"transform\":[\"translate3d(-115.50632%, 0px, 0)\",\"translate3d(0px, 0px, 0)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script 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disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:11.8932%;top:77.02265%;width:76.69903%;height:15.53398%;opacity:1\">\n<div id=\"anim-ca1796c5-579e-4474-aeab-1aa45d2428f6\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:translate3d(-115.50632%, 0px, 0)\">\n<div id=\"anim-06b7fcaa-a706-4c94-9418-2c9f837b8946\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-dd147325-6294-448a-afeb-17fcc279143a\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.15)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6329113924050633% 0.6329113924050633% 0.6329113924050633% 0.6329113924050633% \/ 2.083333333333333% 2.083333333333333% 2.083333333333333% 2.083333333333333%;background-clip:content-box;background-color:#000\" id=\"el-0265250f-9c48-49f9-9412-cf47f527dc4e\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.216455696202532% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.388350em;line-height:1.2;text-align:center;padding:1.2658227848101267% 2.5316455696202533%;color:#000000\"><span><span style=\"color: #fff\">Maths concept note from NCERT: Properties of Determinants<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:46.60194%;top:100.16181%;width:41.74757%;height:4.04531%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:1.1627906976744187% 1.1627906976744187% 1.1627906976744187% 1.1627906976744187% \/ 8% 8% 8% 8%;background-clip:content-box;background-color:#000\" id=\"el-0426ea44-4ece-4990-8257-eb45f3e9b3ea\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:-0.12263808139534883% 0;font-family:&quot;Roboto&quot;,&quot;Helvetica Neue&quot;,&quot;Helvetica&quot;,sans-serif;font-size:0.242718em;line-height:1.2;text-align:initial;padding:2.3255813953488373% 4.651162790697675%;color:#000000\"><span><span style=\"color: #fff\">BY Team Aakash Byju&#8217;s<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:11.65049%;top:0;width:11.65049%;height:7.76699%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-ca15271c-7a41-4133-8444-9a10b7a7d932\">\n<div style=\"position:absolute;width:100%;height:100.00004%;left:0%;top:-0.00002%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/08\/Aakash-Icon-Blue-PNG-1.png\" alt=\"Aakash Icon Blue PNG\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/08\/Aakash-Icon-Blue-PNG-1.png 96w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/08\/Aakash-Icon-Blue-PNG-1-75x75.png 75w\" sizes=\"(min-width: 1024px) 5vh, 12vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"8a887ecb-046b-4837-b6e5-34bd84ea314d\" auto-advance-after=\"7s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-ff23e456-f074-4e6a-be60-55c951d210bb\",\"keyframes\":{\"transform\":[\"translate3d(110.69181%, 0px, 0)\",\"translate3d(0px, 0px, 0)\"]},\"delay\":0,\"duration\":1000,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-71802b8b-973f-4e4d-badb-2d24ca5759ff\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":1000,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-31554fee-ddad-4c6c-a1e4-5d0e8e54228e\",\"keyframes\":{\"transform\":[\"scale(0.15)\",\"scale(1)\"]},\"delay\":0,\"duration\":1000,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#131313\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-35e5c6cf-6586-47c0-b024-a091fc102214\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/determinants-properties2.jpg\" alt=\"determinants properties2\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/determinants-properties2.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/determinants-properties2-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/determinants-properties2-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/determinants-properties2-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:14.56311%;top:65.69579%;width:77.18447%;height:38.83495%;opacity:1\">\n<div id=\"anim-ff23e456-f074-4e6a-be60-55c951d210bb\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:translate3d(110.69181%, 0px, 0)\">\n<div id=\"anim-71802b8b-973f-4e4d-badb-2d24ca5759ff\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-31554fee-ddad-4c6c-a1e4-5d0e8e54228e\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.15)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.628930817610063% 0.628930817610063% 0.628930817610063% 0.628930817610063% \/ 0.8333333333333334% 0.8333333333333334% 0.8333333333333334% 0.8333333333333334%\" id=\"el-641bb672-0b5a-4f67-9424-a5177f4e5403\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.19716981132075437% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.355987em;line-height:1.2;text-align:left;padding:0;color:#000000\"><span><span style=\"color: #fff\">Determinant is defined as a property of a \u201csystem of linear equations.\u201d&nbsp;<\/span><br \/>\n<span style=\"color: #fff\">The determinant \u2018determines\u2019 whether the system has a unique solution or not.<\/span><br \/>\n<span style=\"color: #fff\">Determinant is denoted by Delta or D.<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"c2351c5c-c064-4a59-9e82-8f159fe1ff70\" auto-advance-after=\"7s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-19726bd0-6bc5-488a-a5a6-8dc2c00158f2\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":1000,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-fdcb3241-4720-4d83-9220-07bd09820ff7\",\"keyframes\":{\"transform\":[\"scale(0.3333333333333333)\",\"scale(1)\"]},\"delay\":0,\"duration\":1000,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#27322b\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-2379ba93-a7d2-4f24-b90b-9b0e99dec1fb\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/determinants-properties3.jpg\" alt=\"determinants properties3\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/determinants-properties3.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/determinants-properties3-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/determinants-properties3-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/determinants-properties3-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:11.65049%;top:55.66343%;width:76.69903%;height:38.67314%;opacity:1\">\n<div id=\"anim-19726bd0-6bc5-488a-a5a6-8dc2c00158f2\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-fdcb3241-4720-4d83-9220-07bd09820ff7\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.3333333333333333)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6329113924050633% 0.6329113924050633% 0.6329113924050633% 0.6329113924050633% \/ 0.8368200836820083% 0.8368200836820083% 0.8368200836820083% 0.8368200836820083%\" id=\"el-53aa22a6-fd21-411c-80cc-e8e0a4f6bd8b\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.198417721518987% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.355987em;line-height:1.2;text-align:left;padding:0;color:#000000\"><span><span style=\"color: #fff\">Sign system for order 2, order3, order4,\u2026are shown above.<\/span><br \/>\n<span style=\"color: #fff\">The qualities of determinants are based on the elements, row, and column operations, and they aid in finding the determinant&#8217;s value quickly.<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"bbbbbd3f-9ea4-452f-8560-0ddf572837a0\" auto-advance-after=\"7s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-a6d25149-b5fb-4233-85fe-c4b413a18175\",\"keyframes\":[{\"offset\":0,\"transform\":\"translate3d(0, -1360.05221%, 0)\",\"easing\":\"cubic-bezier(.5, 0, 1, 1)\"},{\"offset\":0.29,\"transform\":\"translate3d(0, 0%, 0)\",\"easing\":\"cubic-bezier(0, 0, .5, 1)\"},{\"offset\":0.45,\"transform\":\"translate3d(0, -382.446681452%, 0)\",\"easing\":\"cubic-bezier(.5, 0, 1, 1)\"},{\"offset\":0.61,\"transform\":\"translate3d(0, 0%, 0)\",\"easing\":\"cubic-bezier(0, 0, .5, 1)\"},{\"offset\":0.71,\"transform\":\"translate3d(0, -130.02099127600002%, 0)\",\"easing\":\"cubic-bezier(.5, 0, 1, 1)\"},{\"offset\":0.8,\"transform\":\"translate3d(0, 0%, 0)\",\"easing\":\"cubic-bezier(0, 0, .5, 1)\"},{\"offset\":0.85,\"transform\":\"translate3d(0, -48.825874339%, 0)\",\"easing\":\"cubic-bezier(.5, 0, 1, 1)\"},{\"offset\":0.92,\"transform\":\"translate3d(0, 0%, 0)\",\"easing\":\"cubic-bezier(0, 0, .5, 1)\"},{\"offset\":0.96,\"transform\":\"translate3d(0, -21.216814476%, 0)\",\"easing\":\"cubic-bezier(.5, 0, 1, 1)\"},{\"offset\":1,\"transform\":\"translate3d(0, 0%, 0)\",\"easing\":\"cubic-bezier(0, 0, .5, 1)\"}],\"delay\":0,\"duration\":1300,\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#284893\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-d8fb7f4d-e83f-4389-8bf3-b86425258220\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/08\/Classroom-Artboard-4.jpg\" alt=\"Classroom-Artboard 4\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/08\/Classroom-Artboard-4.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/08\/Classroom-Artboard-4-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/08\/Classroom-Artboard-4-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/08\/Classroom-Artboard-4-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:14.07767%;top:76.3754%;width:71.35922%;height:6.79612%;opacity:1\">\n<div id=\"anim-a6d25149-b5fb-4233-85fe-c4b413a18175\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:translate3d(0, -1360.05221%, 0)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6802721088435374% 0.6802721088435374% 0.6802721088435374% 0.6802721088435374% \/ 4.761904761904762% 4.761904761904762% 4.761904761904762% 4.761904761904762%;background-clip:content-box;background-color:rgba(0,0,0,0.8)\" id=\"el-7665ef5e-c035-47d9-a2b4-477c53767e84\"><a href=\"https:\/\/byjus.com\/aakash-byjus-free-trial-class\/?utm_source=seobanner&amp;utm_medium=4th-webstory&amp;utm_campaign=freeliveclasses\" data-tooltip-icon=\"https:\/\/cdn1.byjus.comhttps:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2021\/08\/AakashByjus-OG.png\" data-tooltip-text=\"Register Now For Aakash BYJU&#x27;S Free Live Classes\" target=\"_blank\" rel=\"noreferrer noopener\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0\"><\/p>\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:-0.1434948979591837% 0;font-family:&quot;Roboto&quot;,&quot;Helvetica Neue&quot;,&quot;Helvetica&quot;,sans-serif;font-size:0.485437em;line-height:1.2;text-align:center;padding:1.3605442176870748% 2.7210884353741496%;color:#000000\"><span><span style=\"font-weight: 700; color: #fff\">Click Here To<\/span><\/span><\/p>\n<p><\/a><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-page-outlink layout=\"nodisplay\" cta-image=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/08\/Aakash-Icon-Blue-PNG-1.png\" theme=\"dark\"><a href=\"https:\/\/byjus-aakash.onelink.me\/GieR\/aakashwebstories\" rel=\"\">Download Aakash App Now<\/a><\/amp-story-page-outlink><\/amp-story-page><amp-story-page id=\"65309a1e-2b4b-4618-b8d0-6ed69a796062\" auto-advance-after=\"7s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-3db9cc70-41b1-4a7a-b03a-c13349fc1d5b\",\"keyframes\":{\"transform\":[\"translate3d(-115.50632%, 0px, 0)\",\"translate3d(0px, 0px, 0)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-60d88a82-e1ef-4412-be1b-f19b156c5236\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-c4e9ef39-faa6-4053-b383-37b9c788a271\",\"keyframes\":{\"transform\":[\"scale(0.15)\",\"scale(1)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#041f2a\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-1557a80b-0694-46ee-8443-06b3de48f018\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/determinants-properties4.jpg\" alt=\"determinants properties4\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/determinants-properties4.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/determinants-properties4-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/determinants-properties4-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/determinants-properties4-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:11.8932%;top:67.96117%;width:76.69903%;height:30.09709%;opacity:1\">\n<div id=\"anim-3db9cc70-41b1-4a7a-b03a-c13349fc1d5b\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:translate3d(-115.50632%, 0px, 0)\">\n<div id=\"anim-60d88a82-e1ef-4412-be1b-f19b156c5236\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-c4e9ef39-faa6-4053-b383-37b9c788a271\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.15)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6329113924050633% 0.6329113924050633% 0.6329113924050633% 0.6329113924050633% \/ 1.0752688172043012% 1.0752688172043012% 1.0752688172043012% 1.0752688172043012%;background-clip:content-box;background-color:#000\" id=\"el-23838e29-fa46-403a-b837-1f13b809fe85\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.18939873417721506% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.339806em;line-height:1.2;text-align:center;padding:1.2658227848101267% 2.5316455696202533%;color:#000000\"><span><span style=\"font-weight: 700; text-decoration: underline; color: #fff\">Property 1 (interchange property):<\/span><\/p>\n<p><span style=\"color: #fff\">The value of determinant remains same, if it&#8217;s rows and columns are interchanged.<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"ef87003b-9a80-4265-9e0f-b67abe15c678\" auto-advance-after=\"7s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-314bc4fc-0b10-45ef-9de3-5fa9f7b71924\",\"keyframes\":{\"transform\":[\"translate3d(110.75950%, 0px, 0)\",\"translate3d(0px, 0px, 0)\"]},\"delay\":0,\"duration\":1000,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-9251c73d-51bb-4267-9ed1-dc41238b0044\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":1000,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-892ec006-ed41-4489-9214-975ee638a50a\",\"keyframes\":{\"transform\":[\"scale(0.15)\",\"scale(1)\"]},\"delay\":0,\"duration\":1000,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#242424\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-c9ee2ff9-606c-4b47-b3eb-9266d28a8571\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/determinants-properties5.jpg\" alt=\"determinants properties5\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/determinants-properties5.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/determinants-properties5-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/determinants-properties5-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/determinants-properties5-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:15.04854%;top:61.32686%;width:76.69903%;height:32.8479%;opacity:1\">\n<div id=\"anim-314bc4fc-0b10-45ef-9de3-5fa9f7b71924\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:translate3d(110.75950%, 0px, 0)\">\n<div id=\"anim-9251c73d-51bb-4267-9ed1-dc41238b0044\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-892ec006-ed41-4489-9214-975ee638a50a\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.15)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6329113924050633% 0.6329113924050633% 0.6329113924050633% 0.6329113924050633% \/ 0.9852216748768473% 0.9852216748768473% 0.9852216748768473% 0.9852216748768473%\" id=\"el-32006551-6546-48f1-b87f-9eb83889303e\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.18939873417721506% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.339806em;line-height:1.2;text-align:left;padding:0;color:#000000\"><span><span style=\"font-weight: 700; text-decoration: underline; color: #fff\">Property 2 (sign property):<\/span><\/p>\n<p><span style=\"color: #fff\">If any two rows or columns of a determinant are interchanged, the sign of determinant will be changed.<\/span><br \/>\n<span style=\"color: #fff\">But, the numerical value remains unaltered.<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"e2ceefc6-f281-47e0-9ee8-569e5a2410ed\" auto-advance-after=\"7s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-1c2345b6-af58-4ea6-bc41-f125c5246d22\",\"keyframes\":{\"transform\":[\"translate3d(114.87342%, 0px, 0)\",\"translate3d(0px, 0px, 0)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-973b6f69-811c-4ca6-aa4c-5b6b3aaac4c0\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-797b5fd2-f31b-4193-8a36-2a2252b1fe18\",\"keyframes\":{\"transform\":[\"scale(0.15)\",\"scale(1)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#182348\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-08bdb875-2e48-432d-9e72-859c3bc29b19\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/determinants-properties6.jpg\" alt=\"determinants properties6\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/determinants-properties6.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/determinants-properties6-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/determinants-properties6-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/determinants-properties6-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:11.8932%;top:62.45955%;width:76.69903%;height:24.59547%;opacity:1\">\n<div id=\"anim-1c2345b6-af58-4ea6-bc41-f125c5246d22\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:translate3d(114.87342%, 0px, 0)\">\n<div id=\"anim-973b6f69-811c-4ca6-aa4c-5b6b3aaac4c0\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-797b5fd2-f31b-4193-8a36-2a2252b1fe18\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.15)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6329113924050633% 0.6329113924050633% 0.6329113924050633% 0.6329113924050633% \/ 1.3157894736842104% 1.3157894736842104% 1.3157894736842104% 1.3157894736842104%\" id=\"el-790d022a-c111-4935-91df-d128b9310e4c\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.18939873417721506% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.339806em;line-height:1.2;text-align:left;padding:0;color:#000000\"><span><span style=\"font-weight: 700; text-decoration: underline; color: #fff\">Property 3 (Zero property):<\/span><\/p>\n<p><span style=\"color: #fff\">If the elements in any two rows or columns are the same, the determinant&#8217;s value is zero.<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"111a0465-d436-44d1-bf08-a02d7f8aa901\" auto-advance-after=\"7s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-5c6921bb-e12b-4999-aa5b-e8f33cec8b54\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-d67d1fe1-cbcd-446f-bb40-e39f93b6f859\",\"keyframes\":{\"transform\":[\"scale(0.3333333333333333)\",\"scale(1)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#272727\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-dcb8a8a9-05eb-409a-adab-8033494fd09b\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/determinants-properties8.jpg\" alt=\"determinants properties8\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/determinants-properties8.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/determinants-properties8-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/determinants-properties8-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/determinants-properties8-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:11.65049%;top:69.25566%;width:76.69903%;height:26.86084%;opacity:1\">\n<div id=\"anim-5c6921bb-e12b-4999-aa5b-e8f33cec8b54\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-d67d1fe1-cbcd-446f-bb40-e39f93b6f859\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.3333333333333333)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6329113924050633% 0.6329113924050633% 0.6329113924050633% 0.6329113924050633% \/ 1.2048192771084338% 1.2048192771084338% 1.2048192771084338% 1.2048192771084338%\" id=\"el-9673114a-11db-4f3a-b33d-1d92da2e340a\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:1.2148734177215186% 0;font-family:&quot;BioRhyme&quot;,serif;font-size:0.355987em;line-height:1.2;text-align:center;padding:0;color:#000000\"><span><span style=\"font-weight: 700; text-decoration: underline; color: #fff\">Property 4<\/span><\/p>\n<p><span style=\"color: #fff\">If all elements of any row or any column are zero, the determinant value becomes zero.<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"dfe44ea0-5b10-4ba8-99dd-d8512fa263d4\" auto-advance-after=\"7s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-932f72f8-de6a-4bcf-b9bb-b47628ee2e49\",\"keyframes\":{\"transform\":[\"translate3d(-115.50632%, 0px, 0)\",\"translate3d(0px, 0px, 0)\"]},\"delay\":0,\"duration\":1000,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-ee0d429b-5f22-4d75-8b04-18ed1e564039\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":1000,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-e79964e3-8291-454a-9665-fd03f6d4a061\",\"keyframes\":{\"transform\":[\"scale(0.15)\",\"scale(1)\"]},\"delay\":0,\"duration\":1000,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#053b4a\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-9628c63c-6121-44a2-8b3e-18d5aed85382\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/determinants-properties7.jpg\" alt=\"determinants properties7\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/determinants-properties7.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/determinants-properties7-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/determinants-properties7-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/determinants-properties7-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:11.8932%;top:61.65049%;width:76.69903%;height:35.11327%;opacity:1\">\n<div id=\"anim-932f72f8-de6a-4bcf-b9bb-b47628ee2e49\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:translate3d(-115.50632%, 0px, 0)\">\n<div id=\"anim-ee0d429b-5f22-4d75-8b04-18ed1e564039\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-e79964e3-8291-454a-9665-fd03f6d4a061\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.15)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6329113924050633% 0.6329113924050633% 0.6329113924050633% 0.6329113924050633% \/ 0.9216589861751152% 0.9216589861751152% 0.9216589861751152% 0.9216589861751152%\" id=\"el-416bf0a1-2b07-422a-a90b-096de559795c\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.18037974683544256% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.323625em;line-height:1.2;text-align:center;padding:0;color:#000000\"><span><span style=\"font-weight: 700; text-decoration: underline; color: #fff\">Property 5 (multiplication property)<\/span><\/p>\n<p><span style=\"color: #fff\">If each element of a given row or column is multiplied by a constant k, then the value of the new determinant is k times the value of the original determinant.<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"2a4dbf55-f720-4685-9c5e-88853bb39f99\" auto-advance-after=\"7s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-2724b95c-aa72-4148-9a1c-8deb2b3f07e8\",\"keyframes\":{\"transform\":[\"translate3d(115.18987%, 0px, 0)\",\"translate3d(0px, 0px, 0)\"]},\"delay\":0,\"duration\":1000,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-e50c52f3-2e5c-4cdb-bcaa-23fd995dcd9d\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":1000,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-62ebd693-bcf8-46d7-bd72-851b771ba68d\",\"keyframes\":{\"transform\":[\"scale(0.15)\",\"scale(1)\"]},\"delay\":0,\"duration\":1000,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#192349\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-f8d04c4b-e067-4493-b581-6ee6cca05d83\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/determinants-properties9.jpg\" alt=\"determinants properties9\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/determinants-properties9.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/determinants-properties9-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/determinants-properties9-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/determinants-properties9-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:11.65049%;top:66.01942%;width:76.69903%;height:30.09709%;opacity:1\">\n<div id=\"anim-2724b95c-aa72-4148-9a1c-8deb2b3f07e8\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:translate3d(115.18987%, 0px, 0)\">\n<div id=\"anim-e50c52f3-2e5c-4cdb-bcaa-23fd995dcd9d\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-62ebd693-bcf8-46d7-bd72-851b771ba68d\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.15)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6329113924050633% 0.6329113924050633% 0.6329113924050633% 0.6329113924050633% \/ 1.0752688172043012% 1.0752688172043012% 1.0752688172043012% 1.0752688172043012%\" id=\"el-7e940918-56e6-45c0-a312-71dcb66def47\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.198417721518987% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.355987em;line-height:1.2;text-align:center;padding:0;color:#000000\"><span><span style=\"font-weight: 700; text-decoration: underline; color: #fff\">Property 6 (sum property)<\/span><\/p>\n<p><span style=\"color: #fff\">If each element of any row or column consists of two terms, then the determinant can be expressed as the sum of two other determinants.<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"0da78fa1-b2c0-4db0-8ab4-96a64b630790\" auto-advance-after=\"7s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-d6127bfa-f904-4807-a037-505d83d8a444\",\"keyframes\":{\"transform\":[\"translate3d(-115.18988%, 0px, 0)\",\"translate3d(0px, 0px, 0)\"]},\"delay\":0,\"duration\":1000,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-82175aae-93fb-4081-9017-5042792ed465\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":1000,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-e1c4c74b-2729-4057-a3f4-6381fe28a043\",\"keyframes\":{\"transform\":[\"scale(0.15)\",\"scale(1)\"]},\"delay\":0,\"duration\":1000,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#28322b\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-194d412f-c5db-4953-b173-3999f589954f\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/determinants-properties10.jpg\" alt=\"determinants properties10\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/determinants-properties10.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/determinants-properties10-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/determinants-properties10-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/determinants-properties10-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:11.65049%;top:62.62136%;width:76.69903%;height:36.8932%;opacity:1\">\n<div id=\"anim-d6127bfa-f904-4807-a037-505d83d8a444\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:translate3d(-115.18988%, 0px, 0)\">\n<div id=\"anim-82175aae-93fb-4081-9017-5042792ed465\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-e1c4c74b-2729-4057-a3f4-6381fe28a043\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.15)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6329113924050633% 0.6329113924050633% 0.6329113924050633% 0.6329113924050633% \/ 0.8771929824561403% 0.8771929824561403% 0.8771929824561403% 0.8771929824561403%\" id=\"el-9ece0b61-0387-4b22-a81d-3ac1346d7b28\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.18939873417721506% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.339806em;line-height:1.2;text-align:center;padding:0;color:#000000\"><span><span style=\"font-weight: 700; text-decoration: underline; color: #fff\">Property 7<\/span><\/p>\n<p><span style=\"color: #fff\">If all elements of below diagonal or above diagonal or except diagonal elements are zero, then the value of the determinant is equal to product of all diagonal elements.<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><\/amp-story><\/body><\/html><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Determinant is defined as a property of a \u201csystem of linear equations.\u201d The determinant \u2018determines\u2019 whether the system has a unique solution or not.<\/p>\n","protected":false},"author":1,"featured_media":122447,"template":"","meta":{"web_stories_publisher_logo":224678,"web_stories_poster":[],"web_stories_products":[],"footnotes":""},"web_story_category":[2144,2352],"web_story_tag":[2507,2506,2508],"class_list":["post-122194","web-story","type-web-story","status-publish","has-post-thumbnail","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Maths Concept Note from NCERT: Properties of Determinants - Aakash Blog<\/title>\n<meta name=\"description\" content=\"Determinant is defined as a property of a \u201csystem of linear equations.\u201d The determinant \u2018determines\u2019 whether the system has a unique solution or not.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.aakash.ac.in\/blog\/web-stories\/maths-concept-note-from-ncert-properties-of-determinants\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Maths Concept Note from NCERT: Properties of Determinants - Aakash Blog\" \/>\n<meta property=\"og:description\" content=\"Determinant is defined as a property of a \u201csystem of linear equations.\u201d The determinant \u2018determines\u2019 whether the system has a unique solution or not.\" \/>\n<meta property=\"og:url\" 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