Define a relation $R$ on $\mathbb{Z}\times(\mathbb{Z}\setminus\{0\})$ by $(a,b)R(x,y)\iff ay=bx.$
$a)$ Prove that $R$ is an equivalence relation.
$b)$ Describe the equivalence classes corresponding to $R$.
I know that an equivalence relation satisfies transitivity, reflexivity, and symmetry. Also, I know that the Cartesian Product is $A\times B=\{(a,b):a\in A$ and $b\in B\}. $If I could get a hint for $a)$, that would be appreciated. For part $b)$, could someone explain what an equivalence class is? Please refrain from complete solutions. Thank you.