Check the commutativity and associativity of each of the following binary operations: (vii) ‘*’ on Q defined by a * b = a + a b for all a, b ∈ Q (viii) ‘*’ on R defined by a * b = a + b -7 for all a, b ∈ R

(vii)  to check : commutativity of *

Thus, * is not commutative on Q.

to prove : associativity on Q.

Thus, * is not associative on Q.

(viii)  to check: commutativity of *

Thus, * is commutative on R

to prove : associativity of * on R.

Thus, * is associative on R.