Let $A \in \mathbb{C}^{N \times N}$ be a D6159: Complex square matrix such that
(i) | $\lambda \in \mathbb{C}$ is a D1207: Complex number |
(i) | \begin{equation} A = \begin{bmatrix} \lambda & 0 & \cdots & 0 \\ 0 & \lambda & \vdots & 0 \\ \vdots & \cdots & \ddots & \vdots \\ 0 & 0 & \cdots & \lambda \end{bmatrix} \end{equation} |
Then
\begin{equation}
\text{Det} A
= \lambda^N
\end{equation}