Question

$\left(a\right)$ What is the additive inverse of $0$?

$\left(b\right)$ What is the multiplicative inverse of $1$?

$\left(c\right)$ Which integers have their own multiplicative inverses?

Answer 1

$\left(a\right)$ What is the additive inverse of $0$?

If the sum of the two numbers is zero, then each number is the additive inverse of the other number.

Ex: $2+(-2)=0$

Here, the additive inverse of $2$ is $-2$.

Now, the additive inverse of $0$ is $0$. [Since, $0+0=0$

$\left(b\right)$ What is the multiplicative inverse of $1$?

If the product of the two numbers is $1$, then each number is the multiplicative inverse of the other number.

ex: $2\times \frac{1}{2}=1$

Here, the multiplicative inverse of $2$ is $\frac{1}{2}$.

Now, the multiplicative inverse of $1$ is $1$. [Since, $1\times 1=1$]

$\left(c\right)$ Which integers have their own multiplicative inverses?

Since, $1\times 1=1$ and $-1\times -1=1$

So, $1$ and $-1$ have their own multiplicative inverses.