|(adj A)| = | A |2
In general, if A is a square matrix of order n, then |adj(A)| = |A|n – 1 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