Let A be a 3 $\times$ 3 matrix such that $\mathrm{|adj(adj(adj~A))|=12^4}$. Then $\mathrm{|A^{-1}~adj~A|}$ is equal to
Solution
$|A|^{(n-1)^{3}}=12^{4}$
<br/><br/>
$$
\begin{aligned}
&|A|^{8}=12^{4} \\\\
&|A|=\sqrt{12} \\\\
&\left|A^{-1} \operatorname{adj} A\right|=\left|A^{-1}\right| \cdot|A|^{2} \\\\
&=|A| = 2\sqrt3
\end{aligned}
$$
About this question
Subject: Mathematics · Chapter: Matrices and Determinants · Topic: Determinants
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