If A [(1, 2, α), (1, 0, 1), (0, 1, 2)] and Det(Adj (A –2A^T) Adj (2A – A^T)) = 2^8 then det(A)^2 is

Question

If \(A = \begin{bmatrix} 1 & 2 & \alpha \\ 1 & 0 & 1 \\ 0 & 1 & 2 \end{bmatrix}\) and Det(Adj (A –2A^T) Adj (2A – A^T)) = 2⁸ then det(A)² is

Answer 1

Correct answer is : 16

Adj(A - 2A^T) Adj(2A - A^T)| = 2⁸ 

P = A - 2A^T

Q = 2A^T - A ⇒ Q^T = 2A^T - A = - P