I am trying to write an algorithm to rotate a bitmap image of $n$ by $n$ size by an angle $\alpha$.
I know that I have to find a rotation matrix, then perform matrix multiplication of the rotation matrix by the image matrix data input.
I know that the $2\times 2$ rotation matrix is
$$T_\alpha=\left(\begin{array}{cc}\cos\alpha & -\sin\alpha \\ \sin \alpha & \cos \alpha \end{array}\right)$$
However, I am not sure how to find the appropriate $n \times n$ matrix.