First of all, the adjoint of a matrix is described as the transpose of a cofactor matrix of the original matrix. To denote, for a matrix A, the adjoint can be written as adj A. In contrast, the inverse of matrix A is the matrix that, when multiplied by matrix A, gives an identity matrix. The inverse of a Matrix A can be denoted by A-1.
In RD Sharma Solutions for Class 12th Maths Chapter 7, adjoint and inverse of a matrix, students study a topic based on inverse matrices and some of its useful results. A matrix A with dimension n ×n is considered to be invertible only if there exists another matrix B of the same dimension, such that AB=BA=I, where I is denoted as the identity matrix of the same order. Matrices B can be said as the inverse of A. Inverse of matrix A can be symbolically represented as A-1.
Moreover, students are taught how to determine the adjoint and inverse of a matrix and when it satisfies the given matrix equation, the validity of the inverse is confirmed.
Furthermore, some additional topics are being discussed in this chapter in an in-depth manner. One such topic is finding a non-singular matrix when the adjoint is given. After mastering this topic, students are set to learn a concept called Elementary transformation. This can also be said elementary operations of a matrix.
Lastly, they get exposed to a concept called finding the inverse of a matrix by elementary transformation. Students also get to solve problems based on all these topics to enhance their knowledge.