We know that $R$ is a field with the usual addition and usual multiplication. Is the set of extended real numbers also a field with the same operations? What are the additive inverse and multiplicative inverse of $\infty$ in the extended field?
(We know ($\infty-\infty$) is an indeterminate form, so $-\infty$ can't be additive inverse of $\infty$. And $0$ can't be multiplicative inverse of $\infty$ because we have $c.\infty=0$ if $c=0$.)