I'll help you out here:

*You should say either "I have (already) eaten" or "I (already) ate".

--- The first sentence refers to the "Present Perfect Tense": means that you performed the action of "eating" (something) at some time but you don't specify it (in the past)

Example: "I have eaten a piece of cake today!" Or just "I have eaten a piece of cake."

--- The second one refers to the "Simple Past Tense": it means that you performed the action of eating something and you mentioned the time you did it (in the past)

Example: "I ate a piece of cake an hour ago!"

Hope that helps you!