Define inverse matrix and discuss its properties.

The inverse of matrix is another matrix, which on multiplication with the given matrix gives the multiplicative identity. For a matrix A, its inverse is A^-1, and A.A^-1 = I. Let us check for the inverse of matrix, for a matrix of order 2 × 2, the general formula for the inverse of matrix is equal to the adjoint of a matrix divided by the determinant of a matrix.

A = (abcd)

A^-1 = 1ad−bc(d−b−ca)

A^-1 = 1|A|

Adj A

The inverse of matrix exists only if the determinant of the matrix is a non-zero value. The matrix ___ _______ _________ _______ __________ __________ ________ ______ ______ ___.
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