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

##### 1 Answer

Oct 24, 2015

Yes. Just multiply both sides by

#### Explanation:

Matrix multiplication is associative, so if

#B = IB = (A^-1A)B = A^-1(AB) = A^-1(AC) = (A^-1A)C = IC = C#