If `A=[{:(cos q,sin q),(-sin q, cos q):}]` , then variefy that `A^(2)=[{:( cos 2q, sin 2q),(-sin 2q,cos 2 q):}]`

Explanation

To verify that \( A^2 = \begin{pmatrix} \cos 2q & \sin 2q \\ -\sin 2q & \cos 2q \end{pmatrix} \) for the matrix \( A = \begin{pmatrix} \cos q & \sin q \\ -\sin q & \cos q \end{pmatrix} \), we will follow these steps:

### Step 1: Write down the matrix \( A \)
Given:
\[ A = \begin{pmatrix} \cos q & \sin q \\ -\sin q & \cos q \end{pmatrix} \]

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