Let * be a Binary operation defined on N by `a ** b = 2^(ab)`. Prove that * is commutative.

** 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 ** .

Let * be a binary operation on Q defined by a**b=ab+1 . Determine whether * is commutative but not associative.

Let '**' be a binary operation on Q defined by : a**b=(2ab)/(3) . Show that '**' is commutative as well as associative.

Let A=NxN and '*' be a binary operation on A defined by (a,b)*(c,d)=(a+c,b+d) .Prove that '*' is commutative.

Let '**' be a binary operation defined on NxxN by : (a, b)**(c, d)=(a+c,b+d) . Prove that '**' is commutative and associative.

Let ""^(**) be a binary operation on Q, defined by a^(**)b=(3ab)/(5) . Show that ""^(**) is commutative, if it exists.

Let '*' be the binary operation defined on R by a*b = 1 + ab AA a,binR neither commutative nor associative.

Let A = N xx N being the set of natural numbers. Let '*' be a binary operation on A defined by (a,b) * (c,d) = (a+c,b+d). Show that '*' is commutative.

Let A=NxxN and let ** be a binary operation on A defined by (a,b)**(c,d)=(a+c,b+d) . Show that ** is commutative and associative.

Let * be a binary operation on N defined by a*b= 2^(5ab),a b inN .Discuss the commutativity if this binary operation.