Show that $0$ is the identity for addition on $R$ and $1$ is the identity for multiplication on $R$. But there is no identity element for the operations $-: R \times R \rightarrow R$ and $\div : R_* \times R_* \rightarrow R_*$.

(N/A) For addition,$a+0 = 0+a = a$ for all $a \in R$. Thus,$0$ is the identity element for addition.
For multiplication,$a \times 1 = 1 \times a = a$ for all $a \in R$. Thus,$1$ is the identity element for multiplication.
For subtraction,an identity element $e$ must satisfy $a-e = a$ and $e-a = a$ for all $a \in R$. The first implies $e=0$,but the second implies $e=2a$,which is not constant for all $a$. Thus,no identity exists.
For division,an identity element $e$ must satisfy $a \div e = a$ and $e \div a = a$ for all $a \in R_*$. The first implies $e=1$,but the second implies $e=a^2$,which is not constant for all $a$. Thus,no identity exists.