Chapter 6.CE, Problem 1CE

In Exercises $1-8$, answer true or false. Justify your answer by providing a counterexample if the statement is false or an outline of a proof if the statement is true.

If $A$, $B$, and $C$ are $\left(n\times n\right)$ matrices such that $AB=AC$ and $\det \left(A\right)\ne 0$, then $B=C$.