Show that the operation * defined on `Q-{1}` by `a**b=a+b-ab` is abinary operation. Is * commutative and associative? What is the identity element wrt *? Which elements possess inverses?

Is the binary operation ** defined by Q by a**b=(a+b)/2 for all a,b in Q commutative and associative?

Let ** be an operation defined on R by a**b=a+b+2ab . Show that ** is a binary operation on R. examine commutatively, associatively and existence of identity. Find the elements, if any, which have inverses.

Does the operation * defined below on the given set represent a binary operation? : a**b=ab on Z^+

Is * defined on the set A={1,2,3,4,5} by a**b=L.C.M. of a,b in A , a binary operation?

For the binary operation ** defined below, determine whether ** is commutative and associative : On N, define a**b=a^b

Is the binary operation ** defined on Z (set of integers) by the rule a**b=a-b+ab for all a, bin Z commutative ?

For the binary operation ** defined below, determine whether ** is commutative and associative : On Q, define a**b=(ab)/2

For the binary operation ** defined below, determine whether ** is commutative and associative : On Z, define a**b=ab+1

For the binary operation ** defined below, determine whether ** is commutative and associative : On N, define a**b=2^(ab)