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If $A$ is a square matrix of order 3 , then $\left|\operatorname{Adj}\left(\operatorname{Adj} A^2\right)\right|=$
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The correct answer is:
$|A|^8$
$\begin{aligned} & \text {}\left|\operatorname{adj}\left(\operatorname{adj} \mathrm{A}^2\right)\right|= \\ & |\operatorname{adj} \mathrm{A}|=|\mathrm{A}|^{n-1}=|\mathrm{A}|^2 \\ & \left|\operatorname{adj} \mathrm{A}^2\right|=|\operatorname{adj} \mathrm{A}|^2=\left(|\mathrm{A}|^2\right)^2-|\mathrm{A}|^4 \\ & \left|\operatorname{adj}\left(\operatorname{adj} \mathrm{A}^2\right)\right|=\left(|\mathrm{A}|^4\right)^{3-1} \\ & =\left(|\mathrm{A}|^4\right)^2=|\mathrm{A}|^8\end{aligned}$
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