Quote:Multiplying by zero equals zero.
It's true for real numbers algebra.
It's interesting, however, that you could come up with a set and with a binary operation (multiplication) where a, b are not zero yet a*b = 0. For example, in a ring of residues modulo 6: [2]*[3]=[0] (while [2] =/= [0], and [3] =/= [0]). Not going into much details I'd point out that zero here is an additively-neutral element: [a] + [0] = [a] just like a+0=a in case of real numbers.