If A=\begin{bmatrix}2&-1&0\\ -1&3&0\\ 1&0&1\end{bmatrix}, then what is the value of det[adj(adjA)]?

Explanation

First, calculate det(A) = 2(3) - (-1)(-1) = 6 - 1 = 5. For a square matrix of order n, det[adj(adjA)] = (det(A))^{(n-1)^2}. Here n=3, so it evaluates to 5^{(3-1)^2} = 5^4 = 625.

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