Assertion (A): If A = bmatrix 2 & 2 - & bmatrix is a non-singular matrix and A( adj A) =…
Mathematics · Class 12 · CBSE — Determinants
Assertion (A): If \(A = \begin{bmatrix} 2\cos\theta & 2\sin\theta \\ -\sin\theta & \cos\theta \end{bmatrix}\) is a non-singular matrix and \(A(\text{adj } A) = \begin{bmatrix} \alpha & 0 \\ 0 & \alpha \end{bmatrix}\), then \(\alpha = 2\).
Reason (R): \(A(\text{adj } A) = |A| I_n\) where \(I\) is an identity matrix of order \(n\).
- Both (A) and (R) are true and (R) is the correct explanation of (A).
- Both (A) and (R) are true but (R) is not the correct explanation of (A).
- (A) is true but (R) is false.
- (A) is false but (R) is true.
Answer
(A) Both (A) and (R) are true and (R) is the correct explanation of (A).
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