# How can we determine associativity of a binary structure from its Cayley table? [duplicate]

Suppose $S$ is a finite set with a binary operation $*$ given by a Cayley table. While the commutativity of $*$ can be determined on the basis of the symmetry of the table across the upper-left to lower-right diagonal, is there any way we can, by inspecting the table alone, decide if $*$ is associative or not?