Let $I_N \in \mathbb{C}^{N \times N}$ be a D5699: Complex identity matrix.
A D6159: Complex square matrix $A \in \mathbb{C}^{N \times N}$ is invertible if and only if

(1)	$A$ is a D5866: Left-invertible complex matrix
(2)	$A$ is a D5867: Right-invertible complex matrix