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

EAMCETEAMCET 2015

Solution:

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] $
$=\left|A^{2}\right|^{4}=|A|^{8}$