Let $I_M \in \mathbb{C}^{M \times M}$ be a D5699: Complex identity matrix.
A D999: Complex matrix $A \in \mathbb{C}^{N \times M}$ is left-invertible if and only if \begin{equation} \exists \, B \in \mathbb{C}^{M \times N} : B A = I_M \end{equation}