Explanation

We are told that is negative. We don't know whether a in particular is positive or negative, but we can analyze the situation by cases. If a is positive, then b must be negative, in order for to be negative. If a is negative, then b must be positive, in order for to be negative. Similar cases hold when we start with b and consider a: one must be positive and one negative. This means that (C) cannot be true, because ab would only be positive if both numbers were positive or both numbers were negative.

The correct answer is (C).