If `A=[{:(cos alpha,sin alpha),(-sin alpha, cos alpha):}]` and `A^(-1)=A`' then find the value of `alpha`.

Explanation

To solve the problem, we need to show that the matrix \( A \) is equal to its own inverse, which is the same as saying \( A^{-1} = A^T \). Let's go through the solution step by step.

### Step 1: Define the Matrix \( A \)

Given the matrix:
\[
A = \begin{pmatrix}
\cos \alpha & \sin \alpha \\
...