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 + i y) = - x - i y. 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

additive group | additive identity | multiplicative inverse