Question

If \[A = \begin{bmatrix}\cos \alpha & - \sin \alpha \\ \sin \alpha & \cos \alpha\end{bmatrix}\] is identity matrix, then write the value of α.

Answer 1

\[Here, \]

\[A = \begin{bmatrix}\cos \alpha & - \sin \alpha \\ \sin \alpha & \cos \alpha\end{bmatrix} = I\]

\[ \Rightarrow \begin{bmatrix}\cos \alpha & - \sin \alpha \\ \sin \alpha & \cos \alpha\end{bmatrix} = \begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}\]

The corresponding elements of equal matrices are equal .

\[ \therefore \cos \alpha = 1 \]

`⇒ ∝ =0°`