Simplify: $\sin A$ $\begin{bmatrix} \sin A & -\cos A \\ \cos A & \sin A \end{bmatrix} + \cos A$ $\begin{bmatrix} \cos A & \sin A \\ -\sin A & \cos A \end{bmatrix}$
$\begin{bmatrix}
\sin A & -\cos A \\
\cos A & \sin A
\end{bmatrix} = \sin^2 A + \cos^2 A = 1$
$\begin{bmatrix}
\cos A & \sin A \\
-\sin A & \cos A
\end{bmatrix} = \cos^2 A + \sin^2 A = 1$
Therefore, the given expression becomes:
$\sin A \times 1 + \cos A \times 1 = \sin A + \cos A$