The Powers of the Matrix with Cosine and Sine Functions
Problem 567
Prove the following identity for any positive integer $n$.
\[\begin{bmatrix}
\cos \theta & -\sin \theta\\
\sin \theta& \cos \theta
\end{bmatrix}^n=\begin{bmatrix}
\cos n\theta & -\sin n\theta\\
\sin n\theta& \cos n\theta
\end{bmatrix}.\]
Add to solve later 
