Question:
If $A$ is a square matrix such that $A(\operatorname{adj} A)=10 I$, then $|A|=$_____________
Solution:
Given:
$A$ is a square matrix
$A(\operatorname{adj} A)=10 I$
As we know,
$A(\operatorname{adj} A)=|A| I$
$\Rightarrow 10 I=|A| I$
$\Rightarrow|A|=10$
Hence, $|A|=\underline{10}$.
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