If A is a square matrix of order 3 such that |A| = 3,

Question:

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

Solution:

For any square matrix A, we have

$|a d j(a d j A)|=|A|^{(n-1)^{2}}$

$\Rightarrow|a d j(a d j A)|=(3)^{4}=81$

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