Let `**` be a binary operation on the set Z of integers as `a**b=a+b+1`. Then find the identity element:

Let ** be a binary operation on the set Q of rational numbers as follows a**b=a+ab . Is the binary operation commutative and associative ?

Let ** be a binary operation on the set Q of rational numbers as follows a**b=(a-b)^2 . Is the binary operation commutative and associative ?

Let ** be a binary operation on the set Q of rational numbers as follows a**b=a^2+b^2 . Is the binary operation commutative and associative ?

*be a binary operation on Q,defined as a**b=(3ab)/5 Find the identity element of *if any.

Let ** be a binary operation on the set Q of rational numbers as follows a**b=a-b . Check whether * is commutative and associative

ast ' is a binary operation on R defined as aastb=2ab Find the identity element if exists.

A={1,2,3,4,6},ast is a binary operation on A is defined as aastb=HCF of a and b. Find the identity element.

ast ' be a binary operation on NxxN defined as (a,b)ast(c,d)=(ac,bd) Find the identity element of ast if any

Let ast be a binary operation defined on NtimesN by (a,b)ast(c,d)=(a+c,b+d) Find the identity element for ast if it exists.

* be a binary operation on Q,defined as a**b=(3ab)/5 .Show that *is commutative.