Is the empty string and some words of even length are elements of this set?

$ L = \{w \in \{a,b\}^*| \text{the first, the middle, and the last characters of $ w$ are identical}\}$ .

I have my answers, but I need confirmation:

Is the empty string $ \epsilon \in L$ ? Yes. Reason: there is no first, middle, or last character to break the rule.

Words of even length, assuming the first and last characters of them are identical, again, must be in $ L$ , as there is no middle character to break the rule in such words.

This is in the context of theory of computation by the way.