If $A$ is a square matrix of order 3, then $\left|\operatorname{adj}\left(\operatorname{adj}…
If $A$ is a square matrix of order 3, then $\left|\operatorname{adj}\left(\operatorname{adj} A^2\right)\right|$ is equal to
$|A|^2$
$|A|^4$
$|A|^8$
$|A|^{16}$
Solution
Given matrix $\mathrm{A}$ is of order 3 .
We know that,
$|\operatorname{adj}(\operatorname{adj} A)|=|A|^{(n-1)^2}$
Similarly,
$\left|\operatorname{adj}\left(\operatorname{adj} A^2\right)\right|=\left|A^2\right|^{(3-1)^2}$
$\begin{aligned} & =\left|A^2\right|^{2^2}[\because n=3] \\ & =\left|A^2\right|^4=|A|^8\end{aligned}$