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If \( A \) is a matrix of order \( 3 \), such that \( A(\operatorname{adj} A)=10 I \), then \( |\operatorname{adj} A|= \)
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Verified Answer
The correct answer is:
\( 100 \)
Given that $\mathrm{A} \cdot(\mathrm{adj} \mathrm{A})=10 \mid$
We know that, $\mathrm{A} \cdot(\mathrm{adj} \mathrm{A})=|\mathrm{A}| \mid$
So, $|A|=10$
Therefore,
$|a d j A|=|A|^{3-1}=|A|^{2}=10^{2}=100$
We know that, $\mathrm{A} \cdot(\mathrm{adj} \mathrm{A})=|\mathrm{A}| \mid$
So, $|A|=10$
Therefore,
$|a d j A|=|A|^{3-1}=|A|^{2}=10^{2}=100$
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