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Question
If \[A = \begin{bmatrix}\cos \alpha & - \sin \alpha \\ \sin \alpha & \cos \alpha\end{bmatrix}\] is identity matrix, then write the value of α.
Solution
\[Here, \]
\[A = \begin{bmatrix}\cos \alpha & - \sin \alpha \\ \sin \alpha & \cos \alpha\end{bmatrix} = I\]
\[ \Rightarrow \begin{bmatrix}\cos \alpha & - \sin \alpha \\ \sin \alpha & \cos \alpha\end{bmatrix} = \begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}\]
The corresponding elements of equal matrices are equal .
\[ \therefore \cos \alpha = 1 \]
`⇒ ∝ =0°`
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