A) \[\left[ \begin{matrix} \cos \,\theta & -\sin \theta \\ \sin \theta & \cos \theta \\ \end{matrix} \right]\]
B) \[\left[ \begin{matrix} sin\,\theta & \cos \theta \\ \cos \theta & sin\theta \\ \end{matrix} \right]\]
C) \[\left[ \begin{matrix} \cos \,\theta & sin\theta \\ -sin\theta & \cos \theta \\ \end{matrix} \right]\]
D) \[\left[ \begin{matrix} -sin\,\theta & \cos \theta \\ \cos \theta & sin\theta \\ \end{matrix} \right]\]
Correct Answer: A
Solution :
Let \[A=\left[ \begin{matrix} \cos \,\theta & \sin \theta \\ -\sin \theta & \cos \theta \\ \end{matrix} \right]\] Here, \[{{C}_{11}}=\cos \theta ,\,{{C}_{12}}=\sin \theta \] \[{{C}_{21}}=-\sin \theta ,{{C}_{22}}=\cos \theta \] \[\therefore \] adj \[(A)=\left[ \begin{matrix} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \\ \end{matrix} \right]\] \[=\left[ \begin{matrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \\ \end{matrix} \right]\]
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