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KCET · Maths · Definite Integration

If \( A \) is a matrix of order \( 3 \), such that \( A(\operatorname{adj} A)=10 I \), then \( |\operatorname{adj} A|= \)

  1. A \( 10 \)
  2. B \( 10 \mathrm{I} \)
  3. C \( 11 \)
  4. D \( 100 \)
Verified Solution

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,
\(|a d j A|=|A|^{3-1}=|A|^{2}=10^{2}=100\)