## Additive **Inverse**

It states that additive inverse of a number is basically what we add to number for creating the sum of a zero. In other words, we can say that the additive inverse of a variable X is any other number, y until the sum of X+Y is equal to zero.

The additive inverse of the variable X is equal and also opposite in sign to it therefore, Y = -X or vice versa. Example: the additive inverse of negative number 5 is -5. That’s because when we add 5 and -5 then, as a result, we get the answer = 0.

### Additive **Inverse Calculator**

What about this inverse when it comes to a negative number? Using the same approach as earlier, if the variable X is a negative number.

Then the additive inverse of X will be equal and opposite in sign to it. This means that this inverse of a negative number will be positive.

For instance, if the variable X is equal to -12, then the additive inverse of the variable X will be Y = 12. We can check that the sum of X+Y is equal to zero. When X = -12 and Y = 12, than it results in -12 + 12 = 0.

We should note that the additive inverse of 0 is 0. Because zero is the only real number, that is equal to its own additive inverse. It is also the one and only number for which the equation X = -X becomes true.

**Graphical Representation of **Additive **Inverse**

We might also think of the additive inverse visually. Let us consider the real number line. The real number line that we have to draw horizontally, with 0 near the middle.

It has negative numbers to its left and the positive ones on the right side. Two number having opposite signs fall on either side of 0 at equal distance on the number line.

Once we locate the point corresponding to a number X on the number line. Then we are aware that the additive inverse, or the variable -X, will with respect to 0 on the opposite side of the number line.

In fact, point 0 is the middle point between the variable X and its additive inverse -X. For example, when X = 5, then the additive inverse of X will be -5. It is very clear to see that point 0 is the middle point of the segment between -5 and 5.

**Common Example**

For any number we can calculate it by multiplying it with -1: that results in –n = -1 X n. example of rings of the numbers are integers, real numbers, rational numbers, and complex numbers.

**Relation to Subtraction**

It is related closely to the subtraction. This can be seen as an addition to the opposite:

a – b = a + (-b).

Conversely, it is also said to be a subtraction from zero.

-a = 0 – a.

Hence, unary minus sign notation is seen as a shorthand for subtraction with (0) symbol omitted. In correct typography, there should be no space present after unary (-).

**Some Other Properties**

In addition to the identities mentioned above, negation has algebraic properties that are as follows:

−(−a) = a, it is an operation of evolution

−(a + b) = (−a) + (−b)

a − (−b) = a + b

(−a) × b = a × (−b) = −(a × b)

(−a) × (−b) = a × b

Notably, (−a)2 = a2

**Solved Question For You**

**Ques. If ‘a’ is a real number, then a−1 is said to be:**

(A). Inverse of a.

(B). Identity of a.

(C). Transpose of a.

(D). Determinant of a.

**Ans.** (A). Inverse of a.

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