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If \(A\) is a \(3 \times 3\) matrix and \(|A|=2\), then \(\mid \operatorname{Adj}\) \((\operatorname{Adj} A) \mid \operatorname{Adj}(\operatorname{Adj} A)=\)
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Verified Answer
The correct answer is:
\(32 \mathrm{~A}\)
As, adj \(\operatorname{adj}(\mathrm{A})=|A|^{n-2} A\),
where \(n\) is the order of matrix \(A\).
and \(|\operatorname{adj} \operatorname{adj}(A)|=|A|^{(n-1)^2}\)
So, \(|\operatorname{adj} \operatorname{adj} A|(\operatorname{adj} \operatorname{adj} A)=|A|^{(n-1)^2}|A|^{n-2} A\)
\(=2^4 \cdot 2 A=2^5 A=32 A .\)
\([\because|A|=2 \text { and } n=3]\)
Hence, option (a) is correct.
where \(n\) is the order of matrix \(A\).
and \(|\operatorname{adj} \operatorname{adj}(A)|=|A|^{(n-1)^2}\)
So, \(|\operatorname{adj} \operatorname{adj} A|(\operatorname{adj} \operatorname{adj} A)=|A|^{(n-1)^2}|A|^{n-2} A\)
\(=2^4 \cdot 2 A=2^5 A=32 A .\)
\([\because|A|=2 \text { and } n=3]\)
Hence, option (a) is correct.
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