Let R be the relation on the set of ordered pairs of positive integers such that $((a, b), (c, d)) \in R$ if and only if $ad = bc$. Show that R is an equivalence relation.
IMPORTANT: the elements of the set on which the relation is defined are pairs $A = \{(a, b)|a, b \in$ N and the relation $R \subseteq A \times B$ consists of pairs of pairs, i.e. $((3, 1), (6, 2)) \in R$ because $(3)(2) = (1)(6)$.