Let A=Q×Q and let ∗ be a binary operation on A defined by (a,b)∗(c,d)=(ac,b+ad) for (a,b)(c,d)ϵA. Determine, whether ∗ is commutative and associative. Then, with respect to ∗ on A (i) Find the identity element in A (ii) Find the invertible elements of A.

Let A=Q×Q and let ∗ be a binary operation on A defined by (a,b)∗(

1.	Let A=Q×Q and let ∗ be a binary operation on A defined by (a,b)∗(c,d)=(ac,b+ad) for (a,b)(c,d)ϵA. Determine, whether ∗ is commutative and associative. Then, with respect to ∗ on A (i) Find the identity element in A (ii) Find the invertible elements of A.
Answer» Let $A = Q \times Q$ and let $$ be a binary operation on $A$ defined by $(a, b) (c, d) = (a c, b + a d)$ for $(a, b) (c, d) ϵ A$ . Determine, whether $$ is commutative and associative. Then, with respect to $$ on $A$ $(i)$ Find the identity element in $A$ $(i i)$ Find the invertible elements of $A$ .