Find α such that Matrix is Identity

Given:

\[ A = \begin{bmatrix} \cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha \end{bmatrix} \]

\[ A = I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \]

Step 1: Compare Elements

\[ \cos \alpha = 1 \]

\[ \sin \alpha = 0 \]

Step 2: Solve

\[ \alpha = 0 \quad (\text{or multiples of } 2\pi) \]

Final Answer:

\[ \boxed{\alpha = 0} \]