Question

The additive inverse of -1 is ……………

Answer 1

Hint: We will be using the concepts of the number system to solve the problem. We will be using the concept of additive inverse to solve the problem. We know that an additive inverse is a number that when added to the number yields zero.

Complete step-by-step solution:
Now let us try to understand what additive inverse is. Before understanding the additive inverse we should know what is the additive identity. Additive identity is a number which upon adding to any number will give the same number.
i.e. a + additive identity = a, where a is any number.
Now for every real number additive identity is 0 since for any real number a, \[a + 0 = a\].
Now additive inverse of any number is a number which upon adding to the number gives additive identity.
i.e. a + additive inverse of a = additive identity.
Now we know the additive identity is 0.
So, a + additive inverse of a = 0.
Then, the additive inverse of a = - a.
Thus, we can say the additive inverse of any number is negative of that number.
Now, the additive inverse of –1 is,
$ \Rightarrow - \left( { - 1} \right) = 1$

Hence, the additive inverse of –1 is 1.

Note: We should not get confused between Multiplicative inverse and additive inverse.
Additive inverse and Multiplicative inverse are two different concepts. Additive identity is 0 since a + 0 = a, while multiplicative identity is 1. Since $a \times 1 = a$.
Similarly, the additive inverse of a is –a since \[a + \left( { - a} \right) = 0\], whereas the multiplicative inverse of a is $\dfrac{1}{a}$ as $a \times \dfrac{1}{a} = 1$.
Also, note the difference between identity and inverse.