That is a very good question anon. 
A dollar times by 0 can be interpreted as zero lots of a dollar which is certainly nothing (no money anyway)
Now by the same logic 0 times 0 could be said to be zero lots of nothing which means that you cannot have nothing because I just said I have zero lots of nothing.
logically this should/could mean that you have something. Because if you don't have nothing then you must have something.
0*0=0 this is what I have always believed to be true but after this logical examination of the situation perhaps another mathematician would like to comment. 