When you say the opposite can be the multiplication of -2, did you actually mean the multiplication of -1? It's a bit unclear in the example whether the "loss of two" means 1 * -1 = -1 and therefore a relative loss of two, or 1 * -2 = -2 or a relative loss of 3. I always figured opposite meant inverting either the fraction so 2/1 becomes 1/2 or it meant multiplying by -1, effectively toggling the negative sign.
Of course, we assume the scaling term is what's being inverted, but it's important to think about the meaning. There's a hidden parameter for these operations and sometimes making it explicit can be helpful. (I.e., euler's formula, e^ix, is better seen as 1.0 * e^ix. That is, you are starting at 1.0 then doing a rotation.)
