Additive Inverse

The additive inverse of a number a is the number that, when added to a, yields zero.

For example, 5 + (-5) = 0

This number is also known as the opposite (number), sign change, and negation.

For a real number, it reverses its sign: the opposite to a positive number is negative, and the opposite to a negative number is positive.

Additive inverse is closely related to subtraction, which can be viewed as an addition of the opposite:

ab  =  a + (−b).

Conversely, additive inverse can be thought of as subtraction from zero:

a  =  0 − a.

Hence, (-a) is the additive inverse of a , such that a + (-a) = 0.