Proof that $(a, b) \mathrel{R} (c, d)$ iff $ad = bc$ is an equivalence relation Let $X = \{(a,b) \mid a,b \in \Bbb Z; b \ne 0\}$. We define $(a,b)\mathrel R (c,d)$ iff $ad = bc$. Prove that $R$ is an equivalence relation on the set $X$. Which known set do the equivalence classes of the relation form?

Any help on solving this please?

To show this is an equivalence relation, you need to show, for pairs $(a,b),(c,d), (e,f)$:
i)$(a,b)R(a,b)$, for any pair $(a,b)$
ii) If $(a,b)R(c,d)$ , then $(c,d)R(a,b)$
iii)If $(a,b)R(c,d)$ and $(c,d)R(e,f)$ , then $(a,b)R(e,f)$.
Can you see how to it?
Let's set up i): We want to show that, for any pair $(a,b)$ , i.e., for any choice of integers $a,b$ , we have $(a,b)R(a,b)$. This means that, according to the definition of $R$, we have:
$(a,b)R(a,b)$ iff $ab=ba$ . Can you do the rest?
