linear algebra - Prove if $A$ is a square matrix and $AB=AC Rightarrow B=C$, then $A$ is invertible.

Prove: if $A$ is a square matrix and $AB=AC$ implies $B=C$, then $A$ is invertible.

First year linear algebra, haven't gotten to determinants yet so the proof can't use determinants or anything beyond.

Edit: Solved, thanks.

Answer

Consider the equation: $AX = 0$. We show $X = 0$. Write: $AX = A\cdot 0 \to X = 0$. Thus $A$ is invertible.