If A is a square matrix of order 3 × 3 and $|A|= 4$. The value of $|(adj\,A). A|$ is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 64
$\text{Given a }3\times 3\text{ matrix }A\text{ with }|A|=4.$
For any square matrix,
$\text{adj}(A)\,A = |A|\,I$
Taking determinants on both sides:
$|\text{adj}(A)\,A| = |\,|A|\,I\,|$
$= |A|^{3}$
$= 4^{3}$
$= 64$
The value of $\;|(\text{adj}A)\,A|\;$ is $64$.