Let A be a square matrix such that $A(adj. A) =\begin{bmatrix}4&0&0\\0&4&0\\0&0&4\end{bmatrix}$ then find the values of $|adj(adj. A)|$
Answer & explanation
Correct answer: option 4
We know that $A(adj. A) = |A|I_n$
$∴|A|=4$
$|adj. (adj. A)| = |A|^{(n-1)^2} = 4^4 = 256$ $[∵ n=3]$