Question

If $A$ is a square matrix of order 3 and $|A| = 5$, then $|adj A|$ is:

• A. 5
• B. 25
• C. 125
• D. 15

Hint:

Similarly, $|adj(adj A)| = |A|^{(n-1)^2}$.

Answer 1

The Correct Option is B

Step 1: Concept
For a square matrix of order $n$, the identity is $|adj A| = |A|^{n-1}$.
Step 2: Analysis
Given $n = 3$ and $|A| = 5$. $|adj A| = 5^{3-1} = 5^{2}$.
Step 3: Conclusion
$|adj A| = 25$.
Final Answer: (B)