I don't see how can one check associative property in a Cayley table. For contrast, one can find identity element, inverses and commutativity. But how you check associativity?
I understand that associativity $(x \cdot y) \cdot z = x \cdot (y \cdot z)$ gives exactly one output when you take ordered triple $(x, y, z)$ and apply "$\cdot$" but I can't see how it relates to Cayley tables.