Question

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

• A. 5
• B. 125
• C. 25
• D. 625

Answer 1

The Correct Option is B

If A is a square matrix of order 3 and |A| = 5, then we need to find |A adj(A)|.

We know that \(A \cdot adj(A) = |A|I\), where I is the identity matrix.

So, |A adj(A)| = ||A|I|

Since A is of order 3, \(|A| = 5\), and I is the 3x3 identity matrix:

\(|A adj(A)| = |5I| = | \begin{pmatrix} 5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5 \end{pmatrix}|\)

\(|5I| = 5^3 |I| = 5^3 (1) = 125\)

Therefore, |A adj(A)| = 125.

Thus, the correct option is (B) 125.