Commutative and associative

Consider a binary operation. on N defined a ** b = a^3 + b^3. Choose the correct answer. (A) Is ** both associative and commutative? (B) Is ** commutative but not associative? (C) Is ** associative but not commutative? (D) Is ** neither commutative nor associative?

Let * be a binary operation on N defined by a*b = a^(b) for all a,b in N show that * is neither commutative nor associative

On Z, the set of all integers,a binary operation * is defined by a*b=a+3b-4 Prove that * is neither commutative nor associative on Z.

Let 'o' be a binary operation on the set Q_0 of all non-zero rational numbers defined by a\ o\ b=(a b)/2 , for all a ,\ b in Q_0 . Show that 'o' is both commutative and associate (ii) Find the identity element in Q_0 (iii) Find the invertible elements of Q_0 .

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

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

Check the commutativity and associativity of * on Z defined by a*b=a-b for all a,b in Z