Hence the usual 'fact' that anything times 0 is 0 does not only hold for real numbers, but any rings. Therefore, for example, the zero matrix multiplied by any matrix (where the order matches of course) gives a zero matrix (note: square matrices of order n under the usual matrix addition and multiplication also form a ring, check the axioms urself). Furthermore, I didnot assume that multiplication is commutative in my proof, hence u cannot say a*0=0*a, unless u r dealing with a commutative ring (e.g. real numbers). This theorem is interesting because 0 is an additive concept i.e. 0+a=a+0=a by definition, yet it has multiplicative properties. All thanks to the axioms for a ring (or real numbers)