Groups and FieldsMediumGroups and the Group Axioms

Groups and the Group Axioms · Medium problem

A group of order $5$ with identity $0$ has the Cayley table below, with two entries hidden as $X$ and $Y$ .

\begin{array}{c|ccccc} * & 0&1&2&3&4\\\hline 0&0&1&2&3&4\\ 1&1&2&3&X&0\\ 2&2&3&4&0&1\\ 3&3&4&0&1&2\\ 4&4&0&Y&2&3\end{array}

Using the fact that every row and column contains each element exactly once, find $X$ .