Question

Let A be a square matrix of order 3 such that transpose of inverse of A is A itself. Then |adj (adj A)| is equal to

(A) 9

(B) 27

(C) 4

(D) 1

Answer 1

Answer is (D) 1

Given that 

(A^-1)^T = A ⇒ (A^T)^-1 = A ⇒ AA^T = l ⇒ |A| = ± 1

Now, |adjA)| = |A|^{2^2} = |A|⁴ = 1