> [!Definition] Definition (left & right inverse) > Let $A\in \text{Mat}_{mn}$ be a [[Matrix|matrix]]. If the [[Matrix Product|product]] $BA=I_{n}$, for some $B\in \text{Mat}_{lm}$, where $I_{n}$ is the [[Real Identity Matrix|identity matrix]], then we say that $B$ is the left inverse of $A$ whilst $A$ is the right inverse of $B$. >