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The number (-9) is the additive inverse of 9.Inverse operations can also be used to find the additive inverse of a specific number. For example, -9 is the additive inverse of 9 since the sum of -9 and 9 is 0. Additive inverses come in pairs; 9 is the additive inverse of -9, just as -9 is the additive inverse of 9. Any two numbers are additive inverses if they add up to 0.Visualize a pair of additive inverses on the number line. The number 9 and its additive inverse -9 are both nine units away from 0 but on opposite sides of 0. For this reason, -9 is called the opposite of 9, and 9 is the opposite of -9. The opposite of a number may be positive or negative.
Subtraction
For every number, a,there exists a number called the additive inverse, -a, such that a + -a = 0.
The rational numbers form an algebraic structure with respect to addition and this structure is called a group. And it is the property of a group that every element in it has an additive inverse.
It is a fundamental requirement of algebraic structures called groups.