How do you say "I am" or "I did" in Greek?
Not είμαι, but in indignant response to someone, like this:

-Do your homework!
-I am!

or

-Go take a shower.
-I already did!

or

-(sarcastically) Oh, so your dog is really special./Your dog isn't that special.
-She is!/Yes, she is!

It's hard to think of examples that say exactly what I mean, but I hope you understand.

Question

How do you say "I am" or "I did" in Greek?
Not είμαι, but in indignant response to someone, like this:

-Do your homework!
-I am!

or

-Go take a shower.
-I already did!

or

-(sarcastically) Oh, so your dog is really special./Your dog isn't that special.
-She is!/Yes, she is!

It's hard to think of examples that say exactly what I mean, but I hope you understand.

Answer

Hi! Even though "I am" is " είμαι", and "I did" is ”έκανα" in typical translation, sometimes the answer from English to Greek differ according to the question, mainly because after "I am" follows a verb. 
For example, -Are you okay?(Είσαι καλά?)         -Have you done your homework(έκανες τα μαθήματά σου?)
                        -Yes, I am( Ναι,είμαι)                      -I am doing it right now(τα κάνω τώρα)

Hope I helped you a bit

Answer

If you want to agree on something someone says to you, you can repeat the verb they use in a past, present or future tense. It depends on what you want to say.
E.g verb "κάνω"
-Κάνε τα μαθήματά σου
-Τα κάνω (present)
-Τα έκανα (past) ή
-Θα τα κάνω (future)

If you want to disagree you can use "δεν"
-Κάνε τα μαθήματά σου
-Δεν τα κάνω (present)
-Δεν τα έκανα (past) ή
-Δεν θα τα κάνω (future)

I hope it is clear.