KCET · Maths · Definite Integration
If \( A \) is a matrix of order \( 3 \), such that \( A(\operatorname{adj} A)=10 I \), then \( |\operatorname{adj} A|= \)
- A \( 10 \)
- B \( 10 \mathrm{I} \)
- C \( 11 \)
- D \( 100 \)
Answer & Solution
Correct Answer
(D) \( 100 \)
Step-by-step Solution
Detailed explanation
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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