Question

Find the additive inverse of 10
\[\begin{align}
  & \text{a) 0} \\
 & \text{b) -10} \\
 & \text{c) 8} \\
 & \text{d) None of these} \\
\end{align}\]

Answer 1

Hint: Now the additive inverse of any number is the negative of that number. Hence additive inverse of +a where a is any number is equal to –a. Similarly additive inverse of –a where a is any number is +a.

Complete step-by-step answer:
Now let us try to understand what additive inverse is. Before understanding additive inverse we should know what is 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.
Hence, a + additive inverse of a = 0.
Hence, additive inverse of a = - a.
Hence, we can say the additive inverse of any number is negative of that number.
Hence, the additive inverse of 10 is – 10.
So, the correct answer is “Option B”.

Note: We should not get confused in 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 additive inverse of a is –a since a + (-a) = 0, whereas multiplicative inverse of a is $ \dfrac{1}{a} $ as $ a\times \dfrac{1}{a}=1 $ .
Also note the difference between identity and inverse.