$($a$)$ Does $Z_6-$ integers Modulo $6$ with respect to addition and subtraction form a Ring? Does it form a Field? Show

Your steps of answering. $($note: construct both the addition and subtraction tables$).$

$($b$)$ If $Z_6$ in part $($a$)$ is a cyclic group, determine the generator$($s$)$ for this group.