Show that doesn't exist a group $(G,*)$ such that $\mathbb{R}$ is closed under $*$ and the restriction to $\mathbb{R}$ is the usual multiplication 
Show that doesn't exist a group $(G,*)$ such that $\mathbb{R}\subset G$ such that $\mathbb{R}$ is closed under $*$ and the restriction to $\mathbb{R}$ is the usual multiplication of $\mathbb{R}$

My approach was, suposse that group $G$ exist, but I can not determine the restriction to $\mathbb{R}$ is the usual multiplication. Any hint! thanks

In a group, every element that is not the identity has a inverse element. $1$ is the identity element of the group under multiplication. Now, does zero have an inverse in $\mathbb{R}$? That will answer your question.
