If A is a square matrix of order 3 such that |A| = 5, write the value of |adj A|.
Question:

If $A$ is a square matrix of order 3 such that $|A|=5$, write the value of $|\operatorname{adj} A|$.

Solution:

For any square matrix of order n,

$|\operatorname{adj} A|=|A|^{n-1}$

 

$\Rightarrow|\operatorname{adj} A|=|A|^{2}=5^{2}=25$

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