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If $|A|=8$, where $A$ is square matrix of order 3 , then what is $|\operatorname{adj} A|$ equal to?
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The correct answer is:
64
Let $|\mathrm{A}|=8$ and $\mathrm{A}$ is a square matrix of order $3 .$ We know that $|\operatorname{adj} \mathrm{A}|=|\mathrm{A}|^{n-1} . \mathrm{I}$ where
$n^{\prime}$ is the order of the matrix $\mathrm{A}$.
$\therefore|\operatorname{adj} \mathrm{A}|=8^{3-1}=8^{2}=64$
$n^{\prime}$ is the order of the matrix $\mathrm{A}$.
$\therefore|\operatorname{adj} \mathrm{A}|=8^{3-1}=8^{2}=64$
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