Question

If $A=\left[\begin{array}{cc}\cos \mathrm{\alpha }& -\sin \mathrm{\alpha }\\ \sin \mathrm{\alpha }& \cos \mathrm{\alpha }\end{array}\right]$ is identity matrix, then write the value of α.

Answer 1

$$\begin{gathered} \mathrm{Here}, \\ A=\left[\begin{array}{cc}\cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha \end{array}\right]=I \\ \Rightarrow \left[\begin{array}{cc}\cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha \end{array}\right]=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right] \\ \mathrm{The}\mathrm{corresponding}\mathrm{elements}\mathrm{of}\mathrm{equal}\mathrm{matrices}\mathrm{are}\mathrm{equal}. \\ \therefore \cos \alpha =1 \\ \Rightarrow \alpha =0° \end{gathered}$$