You can't technically multiply infinity by anything... multiplication is an arithmetic operation and infinity is not a number. What you are really saying, what is the limit of axb (a times b) as both a and b approach infinity, which is infinity. Like someone else noted, limit is axb as a approaches infinity and b approaches negative infinity is negative infinity. You can really only talk about infinity as a limit of real numbers, because that's all is. The absence of infinity in the real number line is precisely why the reals are not compact.
So, in other terms, no number is higher than infinity, so the answer is infinty.
