Let `A=NxxN` , and let * be a binary operation on `A` defined by `(a ,\ b)*(c ,\ d)=(a d+b c ,\ b d)` for all `(a ,\ b),\ (c ,\ d) in NxxNdot` Show that `A` has no identity element.

Let A=NxxN , and let * be a binary operation on A defined by (a ,\ b)*(c ,\ d)=(a d+b c ,\ b d) for all (a ,\ b),\ (c ,\ d) in NxxNdot Show that: * is commutative on Adot (ii) * is associative on Adot

Let A=Nuu{0}xxNuu{0} and let * be a binary operation on A defined by (a ,\ b)*(c ,\ d)=(a+c ,\ b+d) for all (a ,\ b),\ (c ,\ d) in Adot Show that * is associative on Adot

Let A=Nuu{0}xxNuu{0} and let * be a binary operation on A defined by (a ,\ b) * (c ,\ d)=(a+c ,\ b+d) for all (a ,\ b),\ (c ,\ d) in Adot Show that * is commutative on Adot

Let A=NxN , and let * be a binary operation on A defined by (a , b)*(c , d)=(a d+b c , b d) for all (a , b),c , d) in NxNdot Show that : '*' is commutative on A '*^(prime) is associative on A A has no identity element.

Let A=QxxQ and let ** be a binary operation on A defined by (a ,\ b)*(c ,\ d)=(a c ,\ b+a d) for (a ,\ b),\ (c ,\ d) in A . Then, with respect to ** on A . Find the identity element in A .

Let R_0 denote the set of all non-zero real numbers and let A=R_0xxR_0 . If * is a binary operation on A defined by (a ,\ b)*(c ,\ d)=(a c ,\ b d) for all (a ,\ b),\ (c ,\ d) in Adot Find the identity element in A .

Let A=QxxQ and let * be a binary operation on A defined by (a ,\ b)*(c ,\ d)=(a c ,\ b+a d) for (a ,\ b),\ (c ,\ d) in A . Then, with respect to * on Adot Find the invertible elements of A .

Let A=Q x Q and let * be a binary operation on A defined by (a , b)*(c , d)=(a c , b+a d) for (a , b),(c , d) in Adot Then, with respect to * on A Find the identity element in A Find the invertible elements of A.

Let R_0 denote the set of all non-zero real numbers and let A=R_0xxR_0 . If * is a binary operation on A defined by (a ,\ b)*(c ,\ d)=(a c ,\ b d) for all (a ,\ b),\ (c ,\ d) in Adot Show that * is both commutative and associative on A (ii) Find the identity element in A

Let R_0 denote the set of all non-zero real numbers and let A=R_0xxR_0 . If . is a binary operation on A defined by (a ,\ b)*(c ,\ d)=(a c ,\ b d) for all (a ,\ b),\ (c ,\ d) in Adot Show that . is both commutative and associative on A