# Definition:Inverse Matrix/Left

## Definition

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 $\mathbf A$.