If $A=\left[\begin{array}{l}\cos \frac{2\pi }{33}\sin \frac{2\pi }{33}\\ -\sin \frac{2\pi }{33}\cos \frac{2\pi }{33}\end{array}\right] then{A}^{2017}=$

$Let\theta =\frac{2\pi }{33}\Rightarrow A=\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{array}\right]$

$\Rightarrow A^{2017}=\left[\begin{array}{cc}\cos 2017\theta & \sin 2017\theta \\ -\sin 2017\theta & \cos 2017\theta \end{array}\right]$

$2017\theta =\left(2017\right)\frac{2\pi }{33}=122\pi +\frac{8\pi }{33}\Rightarrow \cos \left(2017\theta \right)=\cos 4\theta ;$

$\sin \left(2017\theta \right)=\sin 4\theta$