Given Group(Non-abelian) Multiplication Table.
Find $ca,bb\text{ and }df$.
$\begin{array}{ l | c r r r r r } * & e & a & b & c & d &f \\ \hline e & e & a & b & c & d & f \\ a & a & b & e & d \\ b&b\\ c&c&&&e&&a\\ d&d\\ f&f\\ \end{array}$
My question:
Is there an algorithm for filling up the empty cells? if there isnt, what is then the best approach?