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Question: Answered & Verified by Expert
If \( A \) is a matrix of order \( 3 \), such that \( A(\operatorname{adj} A)=10 I \), then \( |\operatorname{adj} A|= \)
MathematicsDefinite IntegrationKCETKCET 2014
Options:
  • A \( 10 \)
  • B \( 10 \mathrm{I} \)
  • C \( 11 \)
  • D \( 100 \)
Solution:
1651 Upvotes 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,
$|a d j A|=|A|^{3-1}=|A|^{2}=10^{2}=100$

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