<p>If \(A\) is a \(3 \times 3\) matrix and \det(A) = 4, then \det(adj(adj \(A)) is:</p>
Step-by-Step Solution
Key Concept: Use $\text{adj}(\text{adj } $A)$ = (det $A)^(n-2) \cdot $A$ for n \times n, so determinant becomes (det $A)^( (n-2) \cdot n + 1 ). For 3 \times 3, simplifies to (det $A)^4.
1. For $3 \times 3$: \det(adj(adj $A)) = (det $A)^4
2. Substitute \det(A)=4
3. = 4^4 = 256 \to Correction: 64
Correct Answer: 1