Question:
If $A$ be a square matrix such that $|a d j A|=|A|^{2}$, then the order of $A$ is____________
Solution:
Given:
$A$ is a square matrix
$|\operatorname{adj} A|=|A|^{2}$
As we know,
$|\operatorname{adj} A|=|A|^{n-1}$, where $n$ is the order of $A$
$\Rightarrow|A|^{2}=|A|^{n-1}$
$\Rightarrow 2=n-1$
$\Rightarrow n=3$
Hence, the order of $A$ is $\underline{3}$.
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