How to determine if certain operation is associative based on Cayley table I have the following table and I don't know how to determine if an operation is associative based on the table. Is there an easy way to do it? Or it's just brute force
\begin{array}{|c|c|c|c|c|c|}
\hline
*& a & b & c &d &e \\ \hline
 a& a&b &c&b&d\\ \hline
 b&  b&c &a&e&c\\ \hline
 c& c &a &b&b&a\\ \hline
 d&b&e&b&e&d\\ \hline
 e&d&b&a&d&c\\ \hline
\end{array}
We can see that it's not commutative because $b*e \neq e*b$, but how do we check if it's associative?

Do two "outer products" using the multiplication table (but the dimensions in different orders). Then you compare the resulting outer products element-wise.
