To find the eigenvalues, we solve the equation
$\begin{align*}\det \left(\begin{matrix} 2 - \lambda & i \\ -i & 2 - \lambda \end{matrix} \right) = 0\end{align*}$
Evaluating the determinant, we have
$\begin{align*}(2 - \lambda)^2 - 1 = 0\end{align*}$
So, the eigenvalues are both $1$ and $3$ . Therefore, answer (B) is correct.

Solution to 2008 Problem 86