Let A be a given square matrix. If there exists another matrix B in such a way that, AB = BA = I, where I is the identity matrix whose order is same as A. Then, B is said to be the inverse matrix of A and written as A-1. Thus, AA-1 = In= A-1A.
In general, inverse is the reciprocal matrix of given square matrix. A square matrix A has its inverse, if and only if the determinant of the matrix is non-zero, i.e. IAI $\neq$ 0.