$\left(\begin{array}{cc}\cot \theta & -1 \\ 1 & \cot \theta\end{array}\right)\left(\begin{array}{cc}\cot \theta & 1 \\ -1 & \cot \theta\end{array}\right)^{-1}=\left(\begin{array}{cc}\alpha & -\beta \\ \beta & \alpha\end{array}\right)$ then

• A

  $\alpha=1$ and $\beta=1$.
• B

  $\alpha=1$ and $\beta=0$
• Correct answer
  C

  $\alpha=\cos 2 \theta$ and $\beta=\sin 2 \theta$.
• D

  $\alpha=\cos \theta$ and $\beta=\sin \theta$.

Hence, the correct answer is option: 'C'.