Theorem 4 A square matrix A is invertible if and only if A is nonsingular matrix Proof Let A be invertible matrix of order n and I be the identity matrix of order n Then, there exists a square matrix B of order n such that AB = BA = I
Now
AB = I So AB  = I     or   A  B  = 1    (since I
1, AB
A B )
=
=
This gives
A ≠ 0