More Nullity. To make my entry below even eaiser to understand, I'll summarize it by saying this: Zero does not have a multiplicative inverse.
It's ALWAYS true that 0x = 0. There's a bunch of crap on ring theory that proves this, but people are saying that my example below is too complex.

So..yeah, we won't go into ring theory.
The multiplicative inverse of a number x is the number which when muliplied by x, equals 1.
So, for example, if X equals 5, the multiplicative inverse is 1/5. 5 * (1/5) = 1.

That doesn't work with zero.
Nullity is crap.