MCQ
If $\tan^{-1}(\cot\theta)=2\theta,$ then $\theta$ is equal to:
- A$\frac{\pi}{3 }$
- B$\frac{\pi}{4}$
- ✓$\frac{\pi}{6}$
- DNone of these.
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where $\omega=\frac{-1+ i \sqrt{3}}{2},$ and $I _{3}$ be the identity matrix of order $3$. If the determinant of the matrix $\left( P ^{-1} AP - I _{3}\right)^{2}$ is $\alpha \omega^{2},$ then the value of $\alpha$ is equal to