If `P(x)=[(cosx, sinx),(-sinx, cosx)]`, then show that `P(x).P(y)=P(x+y)=P(y).P(x)`.

Explanation

To show that \( P(x) \cdot P(y) = P(x+y) = P(y) \cdot P(x) \), we will follow these steps:

### Step 1: Define the matrices
Given:
\[ P(x) = \begin{pmatrix} \cos x & \sin x \\ -\sin x & \cos x \end{pmatrix} \]
\[
...