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COMEDK · Maths · 21. Matrices

If \(A\) is a matrix of order \(4 \operatorname{such}\) that \(A(\operatorname{adj} A)=10 \mathrm{~I}\), then \(|\operatorname{adj} A|\) is equal to

  1. A 10000
  2. B 1000
  3. C 10
  4. D 100
Verified Solution

Answer & Solution

Correct Answer

(B) 1000

Step-by-step Solution

Detailed explanation

Given that \(A\) is a square matrix of order \(n = 4\). The property of the adjoint of a matrix states that \(A(\operatorname{adj} A) = |A| I\). Comparing this with the given equation \(A(\operatorname{adj} A) = 10 I\), we find that \(|A| = 10\). The determinant of the adjoint…