#### • Class 11 Physics Demo

Explore Related Concepts

Definition of “ additive-inverse” : The additive-inverse of a number or an expression is another number or expression such that when they are added together, the sum should be equal to zero.
For example, 1 is the additive-inverse of -1. That is because (1) + (-1) = 1 – 1 = 0. Similarly the additive-inverse of x+2 would be –(x+2).
That is because (x+2) + (-(x+2)) = x + 2 + (-x – 2) = x + 2 – x – 2 = x – x + 2 – 2 = 0 + 0 = 0.
Additive-inverse is also called the opposite.
That means, the additive-inverse of a number n is also called the opposite of the number n.

The formula for finding the additive-inverse of a number or expression is as follows:
Ia = -(a), where Ia is the additive-inverse of a and a is any number or expression.
In general terms additive-inverse of any number a is also written as –a.

Suppose there are two numbers a and b that are additive-inverse of each other.
Then by the definition of additive-inverse that we stated above, we can say that,
a + b = 0
Subtracting a from both sides we have:
b = 0 – a
Since the zero (0) on the right side has no value we omit it.
So that now we have:
b = -a
But we know that b is the additive-inverse of a (Ia)
So we can say that : Ia = -a or Ia = - (a)
Hence proved.