how to prove group or not using associative law

Question

Let G=(a,b)*(c,d)=(a+bc,bd), how to prove this is associative or not .i want to prove this is a group using associative law

Answer 1

When F is a field, F×F with the operation
(a b)*(c,d) = (a ÷ bc, cd) is not a group because
(0,1) is the identity but (a,0) does not have an inverse.

Perhaps you mean (a, b)*(c,d) = (ad ÷ bc, cd), b,d /= 0,
the standard construction of the rationals from the integers.

The statement of the problem is vague and confusing for lacking needed details.