# Solve this following

Question:

If $A=\left[\begin{array}{cc}\cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha\end{array}\right]$ then find the least value of $\alpha$ for which $A+A^{\prime}=1$.

Solution:

Given, $A=\left[\begin{array}{lr}\cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha\end{array}\right]$