Let $I_N \in \mathbb{R}^{N \times N}$ be a D5621: Real identity matrix.
A D4571: Real matrix $A \in \mathbb{R}^{N \times N}$ is invertible if and only if

(1)	$A$ is a D5869: Left-invertible real matrix
(2)	$A$ is a D5868: Right-invertible real matrix