Question

Let \( A \) be a \(3 \times 3\) matrix and let \( B = 3A \). If \( |A| = 5 \), then the value of \( \frac{|\text{adj } B|}{|3A|} \) is equal to

• A. \(27 \)
• B. \(125 \)
• C. \(25 \)
• D. \(135 \)
• E. \(81 \)

Hint:

For adjoint: \( |\text{adj }A| = |A|^{n-1} \). For scalar multiple: \( |kA| = k^n |A| \).

Answer 1

The Correct Option is D