**INVERSE OF A MATRIX**

A non-singular square matrix A = [a] of order n is said to be invertible or has an inverse, if there exists another non-singular square matrix B of order no such that AB = BA = In

where, I is an identity matrix of order n. Then, we write B=A-1 or A = B-1

Hence, we say that A-7 is the inverse of A, if AA-1 = A-1 A = 1 The inverse of a matrix A is given by A-1 adj (A) TA 1 a

Note: Non-singular and singular matrices A matrix A is said to be non-singular, if its determinant is non-zero, i.e. Al 6 0. The matrix whose determinant is zero, i.e. Al = 0, is called a singular matrix.