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)	\begin{equation} \exists \, B \in \mathbb{R}^{N \times N} : B A = I_N \end{equation}
(2)	\begin{equation} \exists \, C \in \mathbb{R}^{N \times N} : A C = I_N \end{equation}

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