If \( A=\left(\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array....

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If \( A=\left(\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right) \) then for any \( n \in \mathbb{N}, A^{n} \) equals
\( \mathrm{P} \)
(1) \( \left(\begin{array}{cc}\cos ^{n} \theta & \sin ^{n} \theta \\ -\sin ^{n} \theta & \cos ^{n} \theta\end{array}\right) \)
(2) \( \quad\left(\begin{array}{cc}\cos n \theta & \sin n \theta \\ -\sin n \theta & \cos n \theta\end{array}\right) \)
(3) \( \left(\begin{array}{cc}n \cos \theta & n \sin \theta \\ -n \sin n \theta & n \cos \theta\end{array}\right) \)
(4) None of these


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