Interesting. Yes, if AB = CD and neither A = C = 0 nor B = D = 0, then . Under these assumptions, B = 0 iff C = 0 and A = 0 iff D = 0. Check what happens when B = 0 and C = 0, or when A = 0 and D = 0. The remaining case is when neither of the numbers equals 0. Then AB = CD implies A / C = D / B. Let's call this number x. We have
iff
iff
iff
which is true.