a*b is defined from NxN to N .

As u have rightly pointed out ..there is a problem with the way it has been defined . This is because an even and odd combination will not result in the answer belonging to N.

So the only way to proceed wud be to restate the question itself.(This need not be actually done ..but this seems to be the way out). It could be said ..that in domain we substitute those N for which the result would also belong to N...i.e

both even or both odd. Then we show that it is commutative.