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AP EAMCET · Maths · Matrices

If \(A=\left[\begin{array}{ccc}\cos \alpha & -\sin \alpha & 0 \\ \sin \alpha & \cos \alpha & 0 \\ 0 & 0 & 1\end{array}\right]\), then \((\operatorname{Adj} A)^{-1}=\)

  1. A \(A+I\)
  2. B \(A-I\)
  3. C A
  4. D \(\operatorname{Adj}\left(A^{-1}\right)\)
Verified Solution

Answer & Solution

Correct Answer

(C) A

Step-by-step Solution

Detailed explanation

We have, \[ \begin{aligned} & A=\left[\begin{array}{ccc} \cos \alpha & -\sin \alpha & 0 \\ \sin \alpha & \cos \alpha & 0 \\ 0 & 0 & 1 \end{array}\right] \\ & \therefore|A|=\cos ^2 \alpha+\sin ^2 \alpha=1 \end{aligned} \] Now,…