# Solve this following

Question:

If $A_{\alpha}=\left(\begin{array}{cc}\cos \alpha & \sin \alpha \\ -\sin \alpha & \cos \alpha\end{array}\right)$ then $\left(A_{\alpha}\right)^{2}=?$

A. $\left(\begin{array}{cc}\cos ^{2} \alpha & \sin ^{2} \alpha \\ -\sin ^{2} \alpha & \cos ^{2} \alpha\end{array}\right)$

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

C. $\left(\begin{array}{cc}2 \cos \alpha & 2 \sin \alpha \\ -\sin \alpha & 2 \cos \alpha\end{array}\right)$

D. none of these

Solution: