Question 76 - 2019 (09 Jan Shift 1)

If $A = \begin{bmatrix} \cos\theta & -\sin\theta \ \sin\theta & \cos\theta \end{bmatrix}$, then the matrix $A^{-50}$ when $\theta = \dfrac{\pi}{12}$, is equal to:

(1) $\begin{bmatrix} \dfrac{1}{2} & \dfrac{\sqrt{3}}{2} \ -\dfrac{\sqrt{3}}{2} & \dfrac{1}{2} \end{bmatrix}$

(2) $\begin{bmatrix} \dfrac{\sqrt{3}}{2} & \dfrac{1}{2} \ -\dfrac{1}{2} & \dfrac{\sqrt{3}}{2} \end{bmatrix}$

(3) $\begin{bmatrix} \dfrac{\sqrt{3}}{2} & -\dfrac{1}{2} \ \dfrac{1}{2} & \dfrac{\sqrt{3}}{2} \end{bmatrix}$

(4) $\begin{bmatrix} \dfrac{1}{2} & -\dfrac{\sqrt{3}}{2} \ \dfrac{\sqrt{3}}{2} & \dfrac{1}{2} \end{bmatrix}$