A binary operation `**` be defined on the set R by `a**b = a+b +ab`. Show that `**` is commutative, and it is also Associative.

** be binary operation defined on a set R by a**b=a+b-(ab)^2 . Show that ** is commutative, but it is not associative. Find the identity element for ** .

If ** be binary operation defined on R by a**b = 1 + ab, AA a,b in R . Then the operation ** is (i) Commutative but not associative. (ii) Associative but not commutative . (iii) Neither commutative nor associative . (iv) Both commutative and associative.

** be a binary operation on R defined by a"*"b = (a)/(4)+b/(7) , a,b inR . Show that ** is not commutative and associative.

L A = NxxN and ** be the binary operation on A defined by (a,b) "*" (c,d) = (a+c,b+d) Show that ** is commutative and associative . Find the identity element for ** on A , if any.

Number of binary operations on the set {a,b} are

On R - {-1}, a binary operation ** defined by a"*"b = a + b +ab then find a^(-1) .

Let ** be the binary operation on N defined by a"*"b = H.C.F of a and b . Is ** commutative ? Is ** associative ? Does there exist identity for this binary operation on N ?

Let ** be the binary operation on Q define a**b = a + ab . Is ** commutative ? Is ** associative ?