If A is a square matrix of order 3 , then Adj(Adj.A^2) =

A

is a square matrix of order 3 , then

\mid \operatorname{Adj}(\operatorname{Adj}\left.A^2\right) \mid=

Options

A $|A|^2$
B $|A|^4$
C $|A|^8$
D $|\mathrm{A}|^{16}$

Correct answer

C. $|A|^8$

Step-by-step solution

\left|\operatorname{adj}\left(\operatorname{adj} A^2\right)\right|=|\operatorname{adj} \mathrm{A}|=|\mathrm{A}|^{n-1}=|\mathrm{A}|^2

\left|\operatorname{adj} A^2\right|=|\operatorname{adj} A|^2=\left(|A|^2\right)^2=|A|^4\left|\operatorname{adj}\left(\operatorname{adj} A^2\right)\right|=\left(|A|^4\right)^{3-1}=\left(|A|^4\right)^2=|A|^8

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