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Prove the following

Question:

Let $\mathrm{A}=\left(\begin{array}{cc}\cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha\end{array}\right),(\alpha \in \mathrm{R})$ such that $A^{32}=\left(\begin{array}{cc}0 & -1 \\ 1 & 0\end{array}\right) .$ Then a value of $\alpha$ is

  1. $\frac{\pi}{16}$

  2. 0

  3. $\frac{\pi}{32}$

  4. $\frac{\pi}{64}$


Correct Option: , 4

Solution:

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