CUET · MATHS · PYQ PAPER 2025
Let \(A=\left[\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{array}\right]\), then \(\left(A^{-1}\right)^T\) equals
- A \(\left[\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{array}\right]\)
- B \(\left[\begin{array}{cc}\cos \theta & -\sin \theta \\ -\sin \theta & \cos \theta\end{array}\right]\)
- C \(\left[\begin{array}{cc}-\cos \theta & \sin \theta \\ \sin \theta & -\cos \theta\end{array}\right]\)
- D \(\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right]\)
Answer & Solution
Correct Answer
(A) \(\left[\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{array}\right]\)
Step-by-step Solution
Detailed explanation
\( \det(A) = \cos^2 \theta + \sin^2 \theta = 1 \) \( A^{-1} = \frac{1}{1}\left[\begin{array}{cc}\cos \theta & -(-\sin \theta) \\ -(\sin \theta) & \cos \theta\end{array}\right] = \left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right] \)…
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