$(2)$ For $R$ a finite ring $($but not assuming that the unify $I_R$ exists$),$ with no zero divisors

$($a$)$ Prove that $R$ does have a unity $I_R$

$(5)$ Prove that every nom$-$zero element has a multiplicative inverse.

$($c$)$ Dedace that if $R$ is also commutatine then $R$ is a field.