Question

If $A$ is a square matrix of order 3 , then | adj $\left(\operatorname{adj} A^{2}\right) \mid$ is equal to

• A. $|A |^{2}$
• B. $|A|^{4}$
• C. $|A|^{8}$
• D. $|A|^{16}$

Answer 1

The Correct Option is C

We know that,
$|\operatorname{adj}(\operatorname{adj} A)| =|A|^{(n-1)^{2}}$
$\left|\operatorname{adj}\left(\operatorname{adj} A^{2}\right)\right| =\left|A^{2}\right|^{(3-1)^{2}} $
$=\left|A^{2}\right|^{2} \,\,[\because n=3] $
$=\left|A^{2}\right|^{4}=|A|^{8}$