Let `A = Q xx Q`, where Q is the set of all rational numbers, and * be abinary operation defined on A by `(a, b) * (c, d) = (ac, b + ad)`, for all `(a, b) (c, d) in A`.Find the identity element in A.

Let A = Q xx Q , where Q is the set of all rational numbers and * be a binary operaton on A defined by (a,b) * (c,d) = (ac, ad+b) for all (a,b), (c,d) in A. Then find the identify element of * in A.

Let A=QxxQ , where Q is the set of all rational numbers and '**' be the operation on A defined by : (a,b)**(c,d)=(ac,b+ad)" for "(a,b),(c,d)inA . Then, find : (i) The identity element of '**' in A (ii) Invertible elements of A and hence write the inverse of elements (5, 3) and ((1)/(2),4) .

Let A = Q xx Q , where Q is the set of all natural involved and * be the binary operation on A defined by (a,b)* (c,d) =(ac,b+ad) for (a,b), (c,d) in A. Then find Invertible elements of A, and hence write the inverse of elements (5,3) and (1/2, 4)

Let Q be the set of all rational numbers and * be the binary operation , defined by a * b=a+ab for all a, b in Q. then ,

Let A=NNxxNN , a binary operation ** is defined on A by (a,b)**(c,d)=(ad+bc,bd) for all (a,b),(c,d)inA. Show that ** possesses no identity element in A.

Let S =Q xx Q and let * be a binary operation on S defined by (a, b)* (c,d) = (ac, b+ad) for (a, b), (c,d) in S. Find the identity element in S and the invertible elements of S.

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

Let A=N xx N, and let * be a binary operation on A defined by (a,b)*(c,d)=(ad+bc,bd) for all (a,b),(c,d)in N xx N* 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 A has no identity element.