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