Abstract Algebra

Abstract Algebra Decide whether the indicated operations of addition and multiplication are defined (closed) on the set, and give a ring structure. If a ring is not formed, tell why this is the case. If a ring is formed, state whether the ring is commutative, whether it has unity, and whether it is a field. ga + by(2)|a, be@} with the usual addition and multiplication. Please show using each of the following 11 properties : 1.) (R, +) is closed 2.) (R,+) is associative 3.) (R, +) has the identity 0 4.) Every element of R has the additive inverse : - a 5.) (R,+) is commutative 6.) (R, *) is closed 7.) (R,*) is associative 8.) Left and right distributive law hold 9.) (R, *) is commutaitve 10.) (R,*) has the identity 1 11.) Every element of R has a multiplicative inverse (except 0)