If A = [cosθ sinθ −sinθ cosθ], then the matrix A^−50 when θ=π/12, is equal to :

Question

If $A=\begin{bmatrix}\cos\theta&-\sin\theta\\\sin\theta&\cos\theta\end{bmatrix}$, then the matrix $A^{-50}$ when $\theta={\pi\over12}$, is equal to :

(1) $\begin{bmatrix}{\sqrt3\over2}&{1\over2}\\-{1\over2}&{\sqrt3\over2}\end{bmatrix}$

(2) $\begin{bmatrix}{1\over2}&{\sqrt3\over2}\\-{\sqrt3\over2}&{1\over2}\end{bmatrix}$

(3) $\begin{bmatrix}{1\over2}&-{\sqrt3\over2}\\{\sqrt3\over2}&{1\over2}\end{bmatrix}$

(4) $\begin{bmatrix}{\sqrt3\over2}&-{1\over2}\\{1\over2}&{\sqrt3\over2}\end{bmatrix}$