I just came across this theorem in what is mathematics ? Why is -1 * -1 = 1 and not and not -1 * -1 = -1 Here is the proof ! Law of signs is not something that can be "proved" it is created by us to preserve another law, which we know as distributive law Consider for example a(b+c) = ab + ac and assume that -1 * -1 = -1 Now if we choose a = -1, b = 1 and c = -1 then according to distributive law it LHS should be -1(1-1) = -1(0) = 0 However RHS would give -1(1-1) = -1*1+(-1)*(-1) = -1+(-1) = -2 and hence our distributive law fails That is the reason we use -1*-1 = 1 instead of -1. Got it !