If $A=\left(\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{array}\right)$ and $\theta=\frac{2 \pi}{7}$, then $A^{100}=A \times A \times \ldots .(100$ times $)$ is equal to

• Correct answer
  A

  $\left(\begin{array}{cc}\cos 2 \theta & -\sin 2 \theta \\ \sin 2 \theta & \cos 2 \theta\end{array}\right)$
• B

  $\left(\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{array}\right)$
• C

  $\left(\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right)$
• D

  $\left(\begin{array}{cc}0 & -1 \\ 1 & 0\end{array}\right)$

Hence, the correct answer is option: 'A'.