Let *, be a binary operation on N, the set of natural numbers defined by `a * b = a^b`, for all `a,b in N`. Is * associative or commutative on N?

Let * be a binary operation on N, the set of natural numbers, defined by a*b= a^b for all a , b in Ndot Is '*' associative or commutative on N ?

Let * be a binary operation on N, the set of natural numbers, defined by a*b= a^b for all a , b in Ndot Is '*' commutative on N ?

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

If ** be a binary operation on N (the setof natural numbers) defined by a^(**) b = a^(b) , then find (i) 2 ** 3 (ii) 3 ** 2

Let * be a binary operation on Q_0 (set of non-zero rational numbers) defined by a*b= (3a b)/5 for all a ,\ b in Q_0 . Show that * is commutative as well as associative. Also, find the identity element, if it exists.

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

Let A be a set having more than one element. Let '*' be a binary operation on A defined by a*b=sqrt(a^2 + b^2) for all a , b , in A . Is '*' commutative or associative on A?

The binary operation defined on the set z of all integers as a ** b = |a-b| - 1 is

Let * be a binary operation on Z defined by a*b= a+b-4 for all a ,\ b in Zdot Show that * is both commutative and associative.

Let A be a set having more than one element. Let * be a binary operation on A defined by a*b=a for all a ,\ b in Adot Is * commutative or associative on A ?