Question

Let $A$ be a square matrix of order 3 and $|A|=9$. Then $|adj(adj A)|=$ ________.

• A. 6561
• B. 6564
• C. 6569
• D. 8187
• E. 8164

Hint:

$|adj A| = |A|^{n-1}$.

Answer 1

The Correct Option is A

Step 1: Concept
$|adj(adj A)| = |A|^{(n-1)^2}$ where $n$ is the order.

Step 2: Meaning
$n=3$ and $|A|=9$.

Step 3: Analysis
$|adj(adj A)| = 9^{(3-1)^2} = 9^{2^2} = 9^4$.

Step 4: Conclusion
$9^4 = 81 \times 81 = 6561$. Final Answer: (A)