A) \[\left[ \begin{matrix} \cos 2\theta & -\sin 2\theta \\ \sin 2\theta & \cos 2\theta \\ \end{matrix} \right]\]
B) \[\left[ \begin{matrix} \cos 2\theta & \sin 2\theta \\ \sin 2\theta & -\cos 2\theta \\ \end{matrix} \right]\]
C) \[\left[ \begin{matrix} \cos 2\theta & \sin 2\theta \\ \sin 2\theta & \cos 2\theta \\ \end{matrix} \right]\]
D) \[\left[ \begin{matrix} \cos 2\theta & \sin 2\theta \\ -\sin 2\theta & \cos 2\theta \\ \end{matrix} \right]\]
Correct Answer: D
Solution :
Let \[A=\left[ \begin{matrix} \cos 2\theta & -\sin 2\theta \\ \sin 2\theta & \cos 2\theta \\ \end{matrix} \right]\], \[|A|=1\] \[adj\,(A)=\left[ \begin{matrix} \cos 2\theta & \sin 2\theta \\ -\sin 2\theta & \cos 2\theta \\ \end{matrix} \right]\] \[{{A}^{-1}}=\frac{adj\,(A)}{|A|}=\left[ \begin{matrix} \cos 2\theta & \sin 2\theta \\ -\sin 2\theta & \cos 2\theta \\ \end{matrix} \right]\].You need to login to perform this action.
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