Let A = R × R 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.

Let A = N xx N and ** be the binary opertation on A defined by (a, b) ** (c, d) = (a+c, b+d) . Show that ** is commutative and associative.

Let A=NN 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.

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 N defined by a*b = a^(b) for all a,b in N show that * is neither commutative nor associative

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

Let R_(0) denote the set of all non-zero real numbers and let A=R_(0)xx R_(0) .If * is a binary operation on A defined by (a,b)*(c,d)=(ac,bd) for all (a,b),(c,d)in A* show that * is both commutative and associative on A( ii) Find the identity element in A

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

Let A=NxNa n d^(prime)*' be a binaryoperation on A defined by (a , b)*(C , d)=(a c , b d) for all a , b , c , d , in Ndot Show that '*' is commutative and associative binary operation on A.