Binary Operation Identity Invertible Elements

Which of the following statements is/are true?
Let A = Q × Q, where Q is the set of rational numbers, and * be a binary operation on A defined by (a, b) * (c,d) = (ac, b + ad) for all (a,b), (c,d) ϵ A, then
Statement I : The identity element of * in A is (0,1).
Statement II : Invertible elements of A exists.