If \(A\) is a square matrix of order 3 , then \(\left|\operatorname{Adj}\left(\operatorname{Adj} A^2\right)\right|\) is:
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If \(A\) is a square matrix of order 3 , then \(\left|\operatorname{Adj}\left(\operatorname{Adj} A^2\right)\right|\) is:
✓ Correct answer: c)
\(|A|^8\)
Explanation
\(\text{ As }|adj(adj\mathrm{A})|=|\mathrm{A}{|}^{{(\mathrm{n}-1)}^{2}}\text{,}\\ \text{where }\mathrm{n}\text{ is the order of the determinant. }\\ \text{ So, }\left|adj\left(adj{\mathrm{A}}^{2}\right)\right|={\left|{\mathrm{A}}^{2}\right|}^{(3-1{)}^{2}}\\ ={\left|{\mathrm{A}}^{2}\right|}^{4}=|\mathrm{A}{|}^{8}\)
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