Problem 9 (1993 AJHSME)

Consider the operation $*$ defined by the following table: $\begin{matrix}*&1&2&3&4\\ 1&1&2&3&4\\ 2&2&4&1&3\\ 3&3&4&4&2\\ 4&3&2&1\end{matrix}$ For example, $3 * 2 = 1$. Then $(2 * 4) * (1 * 3) =$ [See figure in original PDF]