# Prove that if A is an invertible matrix and AB = BC then B = C.

ha9981
Prove that if A is an invertible matrix and AB = BC then B = C. I thought the way to approach it was to use A^-1 on the equality AB=BC but then I got stuck. I can't get it so that B is on one side and C alone is on the other.

My Try:
AB = BC
A^-1 AB = A^-1 BC
IB = A^-1BC

Also why does B = C not contradict the statement that "the cancellation law doesn't hold for matrices"?