Find the value of \(\alpha \) if \((\cot {\alpha } - 2) I = I\)

Both (a) and (b)

\((\cot {\alpha } - 2) I = I\)

\((\cot {\alpha } - 2)\begin{bmatrix}
1 & 0\\ 0 & 1\end{bmatrix}= \begin{bmatrix}
1 & 0\\ 0 & 1\end{bmatrix}\)

\(\begin{bmatrix} -2+cot{\alpha}& 0\\ 0 & +2+cot{\alpha} \end{bmatrix}=\begin{bmatrix}
1 & 0\\ 0 & 1\end{bmatrix}\)

By equating the elements component-wise we get

\(\cot {\alpha }- 2 = 1\) \(\cot{\alpha } = 1\)

So, \(\alpha \) = \(\frac{\Pi }{4}\) or \(\frac{5\Pi }{4}\)