Question

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

Answer 1

Yes. Just multiply both sides by `A^(-1)`

Explanation:

Matrix multiplication is associative, so if `AB = AC` and `A` is invertible, then

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