$A = adj(B = adj(adj 4))$ where $|A|\cdot|A| = |A|\cdot|B| = 1$
Step-by-Step Solution
Key Concept: The determinant of the adjugate matrix satisfies $|adj(A)| = |A|^{n-1}$
We have $A = adj(B = adj(adj 4))$. Since $|A| = |A|$ and $|A|\cdot|B| = 1$, and using the property that $|adj(A)| = |A|^{n-1}$ for $n×n$ matrices, we get $|A| = 1$ and $|B| = 1$. Therefore $|A| + |B| = 2$.
Correct Answer: 2