Groups and the Group Axioms · Challenge problem

A set $\{e,a,b\}$ has $e$ as a two-sided identity, so the first row and column of its Cayley table already read $e,a,b$. How many different ways are there to fill in the remaining $4$ entries so that every row and column still contains each of $e,a,b$ exactly once (ignore associativity for this count)?