{"id":176473,"date":"2022-05-31T12:05:00","date_gmt":"2022-05-31T06:35:00","guid":{"rendered":"https:\/\/www.aakash.ac.in\/blog\/?post_type=web-story&#038;p=176473"},"modified":"2022-08-20T01:10:53","modified_gmt":"2022-08-19T19:40:53","slug":"maths-orthogonal-matrix-explained-with-examples-ncert-class-12-chapter-3-concept","status":"publish","type":"web-story","link":"https:\/\/www.aakash.ac.in\/blog\/web-stories\/maths-orthogonal-matrix-explained-with-examples-ncert-class-12-chapter-3-concept\/","title":{"rendered":"Orthogonal Matrix Explained With Examples | NCERT Maths Concept"},"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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7.6923076923076925%;background-clip:content-box;background-color:rgba(0,0,0,0.7)\" id=\"el-aa311f0e-8b37-4a10-a844-9b5bf1850fd1\">\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 Byjus<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:11.8932%;top:69.90291%;width:76.45631%;height:17.79935%;opacity:1\">\n<div id=\"anim-a97b1e6b-83eb-4b2f-ab9b-8053d5bd7992\" 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-96ed23eb-7730-4102-938c-30eefe992c9c\" 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:0.6349206349206349% 0.6349206349206349% 0.6349206349206349% 0.6349206349206349% \/ 1.8181818181818181% 1.8181818181818181% 1.8181818181818181% 1.8181818181818181%\" id=\"el-a2070b2e-1ca3-4dec-b297-67bf154d820a\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.2714285714285704% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.485437em;line-height:1.2;text-align:left;padding:0;color:#000000\"><span><span style=\"color: #edf6f6\">Orthogonal Matrix Explained With Examples&nbsp;<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:14.32039%;top:91.90939%;width:76.45631%;height:4.20712%;opacity:1\">\n<div id=\"anim-d667b7dc-4aaf-4bd0-8544-b3f1f44bcd28\" 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-0e12b5f3-599e-49f8-9b04-d1679dd01da7\" 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:0.6349206349206349% 0.6349206349206349% 0.6349206349206349% 0.6349206349206349% \/ 7.6923076923076925% 7.6923076923076925% 7.6923076923076925% 7.6923076923076925%\" id=\"el-6d2af3e4-2172-4d5e-b83a-056277a7bcf0\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.18999999999999986% 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=\"color: #edf6f6\">NCERT Maths Concept<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:11.8932%;top:89.4822%;width:76.21359%;height:0.80906%;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-02a4a2dc-bbd4-47d5-960e-cd11fd4c4e0b\">\n<div class=\"fill\" style=\"background-color:#000;will-change:transform\"><\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:11.65049%;top:0;width:14.07767%;height:9.38511%;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-c3bf6693-34ec-4d34-8c91-26503bb78213\">\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.png\" alt=\"Aakash Icon Blue PNG\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/08\/Aakash-Icon-Blue-PNG.png 96w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/08\/Aakash-Icon-Blue-PNG-75x75.png 75w\" sizes=\"(min-width: 1024px) 6vh, 14vw\" 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=\"ba32cf7f-c1a0-4cfc-8809-86014de66f4d\" auto-advance-after=\"9s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script 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style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-a1463dab-bdab-46f7-b58f-0601a0ca4d2e\">\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\/05\/44.jpg\" alt=\"44\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/44.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/44-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/44-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/44-150x267.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:6.6343%;width:76.45631%;height:22.49191%;opacity:1\">\n<div id=\"anim-729806fc-c182-42f5-ad7e-261396ef108b\" 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-87deacff-27bc-4a48-b30d-9790db87a628\" 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:0.6349206349206349% 0.6349206349206349% 0.6349206349206349% 0.6349206349206349% \/ 1.4388489208633095% 1.4388489208633095% 1.4388489208633095% 1.4388489208633095%\" id=\"el-f132b5e0-e9cf-46e5-8ecb-4865c4fb24d1\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.20809523809523808% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.372168em;line-height:1.2;text-align:center;padding:0;color:#000000\"><span><span style=\"color: #edf6f6\">&nbsp;Before we study the Orthogonal Matrix, let us understand the definition of the Transpose of a matrix and Identity matrix.<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:-7.52427%;top:32.36246%;width:116.50485%;height:67.47573%;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-2f0cedfd-12da-4e6f-8e41-524a0b85e61c\">\n<div style=\"position:absolute;width:100%;height:204.63628%;left:0%;top:-45.98474%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" 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type=\"application\/json\">[{\"selector\":\"#anim-621e3d0c-3fda-4337-90a3-5332afa269bc\",\"keyframes\":{\"transform\":[\"translate3d(114.92064%, 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-c30895ef-1b27-418e-8a4a-e4125066c58c\",\"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-903414d4-38c4-4601-9cf2-d939cb288fb0\",\"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:#fbfbfa\">\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-0b1dbd0e-9671-4c59-840c-9eefc65741d5\">\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\/05\/33.jpg\" alt=\"33\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/33.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/33-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/33-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/33-150x267.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:12.13592%;top:8.25243%;width:76.45631%;height:27.02265%;opacity:1\">\n<div id=\"anim-621e3d0c-3fda-4337-90a3-5332afa269bc\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:translate3d(114.92064%, 0px, 0)\">\n<div id=\"anim-c30895ef-1b27-418e-8a4a-e4125066c58c\" 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-903414d4-38c4-4601-9cf2-d939cb288fb0\" 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:0.6349206349206349% 0.6349206349206349% 0.6349206349206349% 0.6349206349206349% \/ 1.1976047904191618% 1.1976047904191618% 1.1976047904191618% 1.1976047904191618%\" id=\"el-fca7fa23-9bd7-42ac-a7f5-7a5a8a198e26\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.20809523809523808% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.372168em;line-height:1.2;text-align:center;padding:0;color:#000000\"><span><span style=\"color: #edf6f6\">&nbsp;\u2018Transpose\u2019 of a matrix (say A) is a matrix obtained by interchanging its rows into columns or columns into rows. It can be denoted as <\/span><span style=\"font-weight: 700; color: #edf6f6\">A Transpose.<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:-0.48544%;top:39.32039%;width:99.27184%;height:58.09061%;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-37dca4da-c3dd-4651-bfeb-54683005989e\">\n<div style=\"position:absolute;width:100%;height:202.53792%;left:0%;top:-51.26896%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Orthogonal-Matrix-10-1.png\" alt=\"Orthogonal Matrix-10-1\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Orthogonal-Matrix-10-1.png 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Orthogonal-Matrix-10-1-576x1024.png 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Orthogonal-Matrix-10-1-169x300.png 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Orthogonal-Matrix-10-1-150x267.png 150w\" sizes=\"(min-width: 1024px) 45vh, 99vw\" 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=\"f2f04474-441f-45a1-b97e-75ec8a0c0d41\" auto-advance-after=\"9s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-023da492-236f-4b9e-8c02-b4ccd3ef28cc\",\"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-8b0d5bcd-8b13-4e25-9e23-c4344ce186f7\",\"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:#343434\">\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-6a5f7407-5db6-4747-9a51-9f5980b182f7\">\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\/05\/4-6.jpg\" alt=\"4 (6)\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/4-6.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/4-6-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/4-6-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/4-6-150x267.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:9.2233%;width:76.69903%;height:27.02265%;opacity:1\">\n<div id=\"anim-023da492-236f-4b9e-8c02-b4ccd3ef28cc\" 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-8b0d5bcd-8b13-4e25-9e23-c4344ce186f7\" 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% \/ 1.1976047904191618% 1.1976047904191618% 1.1976047904191618% 1.1976047904191618%\" id=\"el-a689135b-4099-460a-b61c-bf51b8a38bb4\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.2074367088607595% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.372168em;line-height:1.2;text-align:center;padding:0;color:#000000\"><span><span style=\"color: #edf6f6\">\u2018Identity Matrix\u2019 is a square matrix that has 1s on the main diagonal and zeros everywhere else. A 3\u00d73 identity matrix can be written as<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:-18.4466%;top:36.24595%;width:130.58252%;height:87.05502%;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-eb7090d2-fa20-458c-aef9-2ae69c16c563\">\n<div style=\"position:absolute;width:100%;height:177.77776%;left:0%;top:-38.88888%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Orthogonal-Matrix-6-1.png\" alt=\"Orthogonal Matrix-6-1\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Orthogonal-Matrix-6-1.png 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Orthogonal-Matrix-6-1-576x1024.png 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Orthogonal-Matrix-6-1-169x300.png 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Orthogonal-Matrix-6-1-150x267.png 150w\" sizes=\"(min-width: 1024px) 59vh, 131vw\" 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=\"43946efa-4942-4387-b717-5a141e0a7118\" auto-advance-after=\"9s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-e4da9097-4f5b-4eec-a86c-e0671594ad73\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.2, 0.6, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-46e12da4-ec58-49a8-bad3-48cecd496e7e\",\"keyframes\":{\"transform\":[\"translate3d(0px, -188.03965%, 0)\",\"translate3d(0px, 0px, 0)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.2, 0.6, 0.0, 1)\",\"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:#473426\">\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-3e979b04-1ac6-41f6-bf61-78a79c362c0d\">\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\/05\/10.jpg\" alt=\"10\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/10.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/10-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/10-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/10-150x267.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:11.40777%;top:13.1068%;width:76.69903%;height:25.40453%;opacity:1\">\n<div id=\"anim-e4da9097-4f5b-4eec-a86c-e0671594ad73\" 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-46e12da4-ec58-49a8-bad3-48cecd496e7e\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:translate3d(0px, -188.03965%, 0)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6329113924050633% 0.6329113924050633% 0.6329113924050633% 0.6329113924050633% \/ 1.2738853503184715% 1.2738853503184715% 1.2738853503184715% 1.2738853503184715%\" id=\"el-e8af8083-4328-4f4f-93c7-55e6a5a6ec3a\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:-0.520411392405063% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.372168em;line-height:1.4;text-align:center;padding:0;color:#000000\"><span><span style=\"color: #edf6f6\">&nbsp;If the product of a matrix and its transpose results in an identity matrix, we call that matrix an \u2018Orthogonal Matrix\u2019.<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:-7.52427%;top:41.90939%;width:115.29126%;height:71.68285%;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-a05101be-4e01-485f-9c65-7b3f85d344a1\">\n<div style=\"position:absolute;width:100%;height:190.6195%;left:0%;top:-45.30975%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Orthogonal-Matrix-11-1-2.png\" alt=\"Orthogonal Matrix-11-1 (2)\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Orthogonal-Matrix-11-1-2.png 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Orthogonal-Matrix-11-1-2-576x1024.png 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Orthogonal-Matrix-11-1-2-169x300.png 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Orthogonal-Matrix-11-1-2-150x267.png 150w\" sizes=\"(min-width: 1024px) 52vh, 115vw\" 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=\"b23efef2-26d6-41b1-9148-63ed8991b99e\" auto-advance-after=\"9s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-33c9cd90-4399-40c2-a4c8-c313b36425f6\",\"keyframes\":{\"transform\":[\"translate3d(-115.33547%, 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-0d2283b3-9a8a-46f9-b4d8-b5aff6b79aeb\",\"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-e59bf03e-dfe2-4a88-9faa-f57a925c1d35\",\"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-da5489a9-bb94-4ea3-8d4e-dd77d73dbafe\">\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\/05\/2-7.jpg\" alt=\"2 (7)\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/2-7.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/2-7-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/2-7-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/2-7-150x267.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:9.54693%;width:75.97087%;height:17.96117%;opacity:1\">\n<div id=\"anim-33c9cd90-4399-40c2-a4c8-c313b36425f6\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:translate3d(-115.33547%, 0px, 0)\">\n<div id=\"anim-0d2283b3-9a8a-46f9-b4d8-b5aff6b79aeb\" 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-e59bf03e-dfe2-4a88-9faa-f57a925c1d35\" 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:0.6389776357827476% 0.6389776357827476% 0.6389776357827476% 0.6389776357827476% \/ 1.8018018018018018% 1.8018018018018018% 1.8018018018018018% 1.8018018018018018%\" id=\"el-15e26d04-4836-436c-bf0a-c2e9ff0dd2f5\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.2094249201277955% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.372168em;line-height:1.2;text-align:center;padding:0;color:#000000\"><span><span style=\"color: #edf6f6\">Let us see the example that explains whether or not the given matrix is an Orthogonal matrix.<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:1.94175%;top:30.42071%;width:95.63107%;height:69.57929%;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-54087d43-d81b-41ed-b7cc-43760fa18c06\">\n<div style=\"position:absolute;width:100%;height:162.89406%;left:0%;top:-31.44703%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Orthogonal-Matrix-9-1.png\" alt=\"Orthogonal Matrix-9-1\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Orthogonal-Matrix-9-1.png 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Orthogonal-Matrix-9-1-576x1024.png 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Orthogonal-Matrix-9-1-169x300.png 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Orthogonal-Matrix-9-1-150x267.png 150w\" sizes=\"(min-width: 1024px) 43vh, 96vw\" 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=\"5f6d4ac7-d449-4eac-b768-878108025ca3\" auto-advance-after=\"9s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-478e608a-468c-420a-a646-a8a15e483a93\",\"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-8be7bdfa-d8fa-47c2-bd4d-b0684047e610\",\"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-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-beb0f3c0-e6c0-4e30-88ac-0a6c7d4c252f\",\"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-8352aca8-a2ac-4f9b-967b-251c4665ea86\",\"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:#04111d\">\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-9622a506-74bc-4cc2-9cf5-3277db18c124\">\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\/05\/11-1.jpg\" alt=\"11 (1)\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/11-1.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/11-1-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/11-1-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/11-1-150x267.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:0;width:76.69903%;height:4.85437%;opacity:1\">\n<div id=\"anim-478e608a-468c-420a-a646-a8a15e483a93\" 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-8be7bdfa-d8fa-47c2-bd4d-b0684047e610\" 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% \/ 6.666666666666667% 6.666666666666667% 6.666666666666667% 6.666666666666667%\" id=\"el-00d57aa2-6e0c-4ba1-84de-4405a10af2b4\">\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:0;color:#000000\"><span><span style=\"font-weight: 700; color: #edf6f6\">Consider a matrix<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:9.95146%;top:6.14887%;width:76.21359%;height:31.06796%;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-871c38a5-3f24-44f1-9ff7-02ff1aadee8f\">\n<div style=\"position:absolute;width:100%;height:290.74074%;left:0%;top:-67.85969%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Orthogonal-Matrix-9-1.png\" alt=\"Orthogonal Matrix-9-1\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Orthogonal-Matrix-9-1.png 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Orthogonal-Matrix-9-1-576x1024.png 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Orthogonal-Matrix-9-1-169x300.png 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Orthogonal-Matrix-9-1-150x267.png 150w\" sizes=\"(min-width: 1024px) 34vh, 76vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:11.65049%;top:42.23301%;width:76.69903%;height:17.96117%;opacity:1\">\n<div id=\"anim-beb0f3c0-e6c0-4e30-88ac-0a6c7d4c252f\" 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-8352aca8-a2ac-4f9b-967b-251c4665ea86\" 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% \/ 1.8018018018018018% 1.8018018018018018% 1.8018018018018018% 1.8018018018018018%\" id=\"el-2a15f2fb-a01d-4d96-9692-40a99ee19cf2\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.2074367088607595% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.372168em;line-height:1.2;text-align:center;padding:0;color:#000000\"><span><span style=\"color: #edf6f6\">The transpose of this matrix is written by interchanging the rows into columns or vice versa.<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:9.95146%;top:62.29773%;width:80.09709%;height:38.34951%;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-ea17118b-61a3-4303-a025-54ff1a7bf120\">\n<div style=\"position:absolute;width:100%;height:247.53872%;left:0%;top:-73.76936%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Orthogonal-Matrix-10-1.png\" alt=\"Orthogonal Matrix-10-1\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Orthogonal-Matrix-10-1.png 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Orthogonal-Matrix-10-1-576x1024.png 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Orthogonal-Matrix-10-1-169x300.png 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Orthogonal-Matrix-10-1-150x267.png 150w\" sizes=\"(min-width: 1024px) 36vh, 80vw\" 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=\"feb509bf-ec63-4311-a23c-af61c07855d3\" auto-advance-after=\"9s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-821d71c8-f8ff-425c-9d2f-f5b1d6b59b20\",\"keyframes\":{\"opacity\":[1,1]},\"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-a4430165-57aa-460c-a38d-8ad0f1979554\",\"keyframes\":{\"transform\":[\"scale(3)\",\"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:#f9fbfb\">\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-6fa92627-08fd-42e2-95cb-646dd3f1cf63\">\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\/05\/58.jpg\" alt=\"58\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/58.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/58-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/58-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/58-150x267.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:11.40777%;top:0;width:76.69903%;height:13.59223%;opacity:1\">\n<div id=\"anim-821d71c8-f8ff-425c-9d2f-f5b1d6b59b20\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:none\">\n<div id=\"anim-a4430165-57aa-460c-a38d-8ad0f1979554\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(3)\">\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% \/ 2.380952380952381% 2.380952380952381% 2.380952380952381% 2.380952380952381%\" id=\"el-6eb361f1-75b8-46ce-bdec-1d65a5ebdf4b\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.2074367088607595% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.372168em;line-height:1.2;text-align:center;padding:0;color:#000000\"><span><span style=\"color: #edf6f6\">Now find the production A and A transpose and see what is the result.<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:-6.31068%;top:15.21036%;width:112.62136%;height:80.58252%;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-f752b411-d29d-4c4c-a8df-01957dcdcac3\">\n<div style=\"position:absolute;width:100%;height:165.64035%;left:0%;top:-32.82017%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Orthogonal-Matrix-8-1-1.png\" alt=\"Orthogonal Matrix-8-1 (1)\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Orthogonal-Matrix-8-1-1.png 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Orthogonal-Matrix-8-1-1-576x1024.png 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Orthogonal-Matrix-8-1-1-169x300.png 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Orthogonal-Matrix-8-1-1-150x267.png 150w\" sizes=\"(min-width: 1024px) 51vh, 113vw\" 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id=\"anim-fff5b6f9-bc57-4b97-a95b-7d9dd3591236\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:none\">\n<div id=\"anim-0ae85a1d-efb8-433e-bc7d-5280a8aaa01a\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(3)\">\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% \/ 2.197802197802198% 2.197802197802198% 2.197802197802198% 2.197802197802198%\" id=\"el-87325a52-3d25-4346-9547-86ac8fabf200\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.22547468354430336% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.404531em;line-height:1.2;text-align:center;padding:0;color:#000000\"><span><span style=\"font-weight: 700; color: #fff\">What an amazing topic it is! Share these facts with your friends.<\/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><\/body><\/html><\/p>\n","protected":false},"excerpt":{"rendered":"<p> \u2018Transpose\u2019 of a matrix (say A) is a matrix obtained by interchanging its rows into columns or columns into rows. It can be denoted as A transpose.<\/p>\n","protected":false},"author":1,"featured_media":176540,"template":"","meta":{"web_stories_publisher_logo":224645,"web_stories_poster":[],"web_stories_products":[],"footnotes":""},"web_story_category":[2144,2352],"web_story_tag":[3443],"class_list":["post-176473","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>Orthogonal Matrix Examples: NCERT Class 12 Maths Chapter 3 Explained<\/title>\n<meta name=\"description\" content=\"Orthogonal Matrix Examples: A square matrix with real numbers or elements is said to be an orthogonal matrix if its transpose is equal to its inverse matrix. here are few examples and more on aakash.ac.in\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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style=\"color: #edf6f6\">Orthogonal Matrix Explained With 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