Question

Which equation illustrates the additive inverse property?

Answer 1

In an additive group G, the additive inverse of an element a is the element a^, such that a+a^, = a^,+a = 0, where 0 is the additive identity of G. Usually, the additive inverse of a is denoted -a, as in the additive group of integers Z, of rationals Q, of real numbers R, and of complex numbers C, where -(x+iy) = -x-iy. The same notation with the minus sign is used to denote the additive inverse of a vector,
v = (0, 2, -3)==>-v = (0, -2, 3),
of a polynomial,
P(x) = x^4+2x^2-1==>-P(x) = -x^4-2x^2+1,
of a matrix
A = [ 1. | 0
-4. | 1.5]==>-A = [-1. | 0
4. | -1.5],
and, in general, of any element in an abstract vector space or a module.