1. If we have (a, b) R (a, b) since ab = ab. The relation is reflexive
2. If we have (a, b) R (c, d) then we have ad = bc. Accordingly, bc = ad yields (c, d) R (a, b). The relation is symmetric.
3. If we have (a, b) R (c, d) and (c, d) R (e, f), we get ad = bc and cf = de.
This implies,
(ad)(cf) = (bc)(de) => af = be
By canceling cd from both sides we got the last result .