Let G $=\{($a$,$b$)$: a$,$b element of R$,$ a not equal to $0\}.$ Define a binary operation $*$ on G by $($a$,$b$)*($c$,$d$)=($ac$,$ b$+$d$)$ for all $($a$,$b$),($c$,$d$)$ element of G$.$ Show that $($G$,*)$ is a group.