αὐτὸς, αὐτὴ, and αὐτὸ

Χαίρετε!

I am getting my first introduction to αὐτὸς, αὐτὴ, and αὐτὸ. If one of these pronouns is the object of an infinitive, is it always in the dative or does it depend on the verb?

It depends on the verb.

Ευχαριστώ!