Let A be a nonsingular square matrix of order 3 × 3. Then |adj A| is equal to

Let A be a nonsingular square matrix of order 3 × 3. Then |adj A| is equal to 

(A) |A|                         (B) |A|²                        (C) |A|³                       (D) 3|A|

We have the formula

Use property of determinant A.adj A = AI

Take mode both sides we get

|A.adj A| = |AI|

As A is matrix of 3x3 hence

 |AI| = A³I

Hence

|A| |adj A| = |A|³

divide by |A| both side we get

|adj A| = |A²|

Hence option B is correct