Let A=Q×Q, where Q is the set of all rational numbers, and ∗ is a binary operation on A defined by (a,b)∗(c,d)=(ac,b+ad) for (a,b),(c,d)∈A. Then find (i) The identity element of ∗ in A. (ii) Invertible elements of A, and hence write the inverse of elements (5,3) and (12,4).

Let A=Q×Q, where Q is the set of all rational numbers, and ∗ is a b

1.	Let A=Q×Q, where Q is the set of all rational numbers, and ∗ is a binary operation on A defined by (a,b)∗(c,d)=(ac,b+ad) for (a,b),(c,d)∈A. Then find (i) The identity element of ∗ in A. (ii) Invertible elements of A, and hence write the inverse of elements (5,3) and (12,4).
Answer» Let $A = Q \times Q$ , where $Q$ is the set of all rational numbers, and $$ is a binary operation on $A$ defined by $(a, b) (c, d) = (a c, b + a d)$ for $(a, b), (c, d) \in A$ . Then find (i) The identity element of $*$ in $A .$ (ii) Invertible elements of $A,$ and hence write the inverse of elements $(5, 3)$ and $(\frac{1}{2}, 4)$ .