If A is a square matrix of order 3 × 3 and $|A|= 4$. The value of $|(adj\,A). A|$ is

64

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 $64$.