Determine whether `*` on `Q` defined by `a*b=(a+b)/2` for all `a ,\ b in Q` is associative or commutative?

Determine whether * on Q defined by a*b=(a+b)/2 for all a ,\ b in Q is commutative?

Determine whether * on N defined by a * b=1 for all a ,\ b in N is associative or commutative?

Determine whether * on N defined by a*b=1 for all a,b in N is associative or commutative?

Check the commutativity of * on Q defined by a*b=a b^2 for all a ,\ b in Q .

Check the commutativity of * on Q defined by a*b=(a-b)^2 for all a ,\ b in Q .

Check the commutativity of * on Q defined by a*b=a-b for all a ,\ b in Q .

A binary operation * on Z defined by a*b= 3a+b for all a ,\ b in Z , is (a) commutative (b) associative (c) not commutative (d) commutative and associative

Check the commutativity of * on Q defined by a*b=a+a b for all a ,\ b in Q .

Let * be a binary operation on Q-{0} defined by a*b=(a b)/2 for all a ,\ b in Q-{0} . Prove that * is commutative on Q-{0} .

A binary operation * on Z defined by a*b=3a+b for all a,b in Z, is (a) commutative (b) associative (c) not commutative (d) commutative and associative