Question
$\text{If A} = \begin{bmatrix} \cos\alpha & \sin\alpha \\ -\sin\alpha & \cos\alpha \\ \end{bmatrix}. \text{find } \alpha \text{ satisfying } 0 < \alpha < \frac{\pi}{2} \text{when A+ A}^{\text{T}} = \sqrt{2}\text{ I}_{2} : $ where $\text{A}^{\text{T}}$ is transpose of $\text{A}$