huge color(purple)(a+(-a)=(-a)+a=0)

-a is called the additive inverse of a.

Inverse property is true for any real number a.

Notice, that we wrote, that a+(-a)=(-a)+a. This is true, according to the commutative property of addition.

Example 1. Additive inverse of 5/3 is -5/3, because 5/3+(-5/3)=0.

Example 2. Additive inverse of -sqrt(2) is sqrt(2), because (-sqrt(2))+sqrt(2)=0.

Example 3. 2.57+(-2.57)=(-2.57)+2.57=0.

Conclusion. Additive inverse of the number (a) is a number, that has the same value as a, but different sign, i.e. -a.