\begin{definition}[Definition:Inverse Matrix/Left]
Let $m, n \in \Z_{>0}$ be a (strictly) positive integer.
Let $\mathbf A = \sqbrk a_{m n}$ be a matrix of order $m \times n$.
Let $\mathbf B = \sqbrk b_{n m}$ be a matrix of order $n \times m$ such that:
:$\mathbf B \mathbf A = I_n$
where $I_n$ denotes the unit matrix of order $n$.
Then $\mathbf B$ is known as a '''left inverse (matrix)''' of $\mathbf A$.
\end{definition}