# If A, B, and C are nxn invertible matrices, does AB=AC mean B = C?

Yes. Just multiply both sides by ${A}^{- 1}$
Matrix multiplication is associative, so if $A B = A C$ and $A$ is invertible, then
$B = I B = \left({A}^{-} 1 A\right) B = {A}^{-} 1 \left(A B\right) = {A}^{-} 1 \left(A C\right) = \left({A}^{-} 1 A\right) C = I C = C$