Inversion of Matrix

     Date:13/12/2023          23UCM004                          Inverse of Matrix

The inverse of a square Matrix A is denoted by A-1

. A

-1 is unique. A-1 exists if and only if 

A is non singular. |A| ≠ 0.

Formula:

A.             

-1 =     

1

|𝐴|

(𝑎𝑑𝑗 𝐴).

The inverse of a square Matrix A is deno

     The inverse of a matrix is another matrix that, when multiplied by the given matrix, yields the multiplicative identity. For a matrix A, its inverse is A^-1. And A.A^-1 = I, where I is denoted as the identity matrix.

            In order to find the inverse matrix, the square matrix must be non-singular and have a determinant value that is not zero. Let us consider a 2×2 square matrix A.

The determinant of matrix A is denoted as ad-bc, and the value of the determinant should not be zero in order for the inverse matrix of A to exist. A simple formula can be used to calculate the inverse of a 2×2 matrix. Furthermore, in order to obtain the inverse of a 3×3 matrix, we must first determine the determinant and adjoint of the matrix.

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