If \( P(x)=\left[\begin{array}{cc}\cos x & \sin x \\ -\sin x & \cos...

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If \( P(x)=\left[\begin{array}{cc}\cos x & \sin x \\ -\sin x & \cos x\end{array}\right] \), then show that
\( \mathrm{P} \)
\[
P(x) \cdot P(y)=P(x+y)=P(y) \cdot P(x) \text {. }
\]
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