Let $A \in \mathbb{R}^{N \times N}$ be a D6160: Real square matrix such that

(i)	$\lambda \in \mathbb{R}$ is a D993: Real number
(ii)	$I_N \in \mathbb{R}^{N \times N}$ is a D5621: Real identity matrix
(iii)	$A = \lambda I_N$

Then \begin{equation} \text{Det} A = \lambda^N \end{equation}