If `A=[[cos alpha,-sin alpha],[sin alpha,cos alpha]],` then for what value of `alpha` is `A` an identity matrix?

Explanation

To find the value of \( \alpha \) for which the matrix \( A = \begin{pmatrix} \cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha \end{pmatrix} \) is an identity matrix, we need to set \( A \) equal to the identity matrix \( I = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} \).

### Step 1: Set the matrices equal
We start by equating the matrix \( A \) to the identity matrix \( I \):
\[ \begin{pmatrix} \cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha \end{pmatrix} = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} \]

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