Let $A \in \mathbb{R}^{2 \times 2}$ be a D4571: Real matrix such that
| (i) | \begin{equation} A = \begin{bmatrix} 0 & - 1 \\ 1 & 0 \end{bmatrix} \end{equation} |
Then
| (1) | \begin{equation} \left\{ \lambda \in \mathbb{R} : \text{det}(A - \lambda I_2) = 0 \right\} = \emptyset \end{equation} |
| (2) | \begin{equation} \left\{ \lambda \in \mathbb{C} : \text{det}(A - \lambda I_2) = 0 \right\} = \{ -i, i \} \end{equation} |