If \( A = \begin{pmatrix} 1 & 2 & 2 \\ 2 & 1 & 1 \\ 1 & 2 & 1 \end{pmatrix} \), then \( |\text{Adj}(A^2)| = \)
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To solve problems involving determinants of adjugates, remember the key formula: \( |\text{Adj}(M)| = |M|^{n-1} \). Combining this with \(|AB| = |A||B|\) allows you to solve for complex expressions like \(|\text{Adj}(A^k)|\) efficiently without computing the matrices \(A^k\) or their adjugates.