Question:
If $A=\left[\begin{array}{cc}\cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha\end{array}\right]$ is identity matrix, then write the value of $\alpha$.
Solution:
Here,
$A=\left[\begin{array}{cc}\cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha\end{array}\right]=I$
$\Rightarrow\left[\begin{array}{cc}\cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha\end{array}\right]=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$
The corresponding elements of equal matrices are equal.
$\therefore \cos \alpha=1$
$\Rightarrow \alpha=0^{\circ}$
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