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If \( A=\left[\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{array}\right] \), then the matrix \( A^{-50} \) when \( \theta=\frac{\pi}{12} \), is equal to :
\( \mathrm{P} \)
W)
(1) \( \left[\begin{array}{cc}\frac{1}{2} & -\frac{\sqrt{3}}{2} \\ \frac{\sqrt{3}}{2} & \frac{1}{2}\end{array}\right] \)
(2) \( \left[\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2}\end{array}\right] \)
(3) \( \left[\begin{array}{rr}\frac{\sqrt{3}}{2} & -\frac{1}{2} \\ \frac{1}{2} & \frac{\sqrt{3}}{2}\end{array}\right] \)
(4) \( \left[\begin{array}{cc}\frac{1}{2} & \frac{\sqrt{3}}{2} \\ -\frac{\sqrt{3}}{2} & \frac{1}{2}\end{array}\right] \)
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