Show that $-a$ is the inverse of $a$ for the addition operation '$+$' on $R$ and $\frac{1}{a}$ is the inverse of $a \neq 0$ for the multiplication operation '$\times$' on $R$.

(N/A) For the addition operation '$+$' on the set of real numbers $R$,the identity element is $0$.
Since $a + (-a) = 0$ and $(-a) + a = 0$,it follows that $-a$ is the additive inverse of $a$.
For the multiplication operation '$\times$' on the set of non-zero real numbers $R \setminus \{0\}$,the identity element is $1$.
Since $a \times \frac{1}{a} = 1$ and $\frac{1}{a} \times a = 1$ for $a \neq 0$,it follows that $\frac{1}{a}$ is the multiplicative inverse of $a$.