How would I answer this question?

Question: 아침 드셨습니까?

Answer: 네, 먹었습니다. 

Thank you!

아침 드셨습니까? means Did you have breakfast? Therefore, If you had breakfast, you would say'네, 아침 먹었습니다 or just 먹었습니다 (먹었어요) is fine. If you didn't have breakfast,you would say '아니요, 아침 안먹었습니다(안먹었어요). You can also say '못'먹었습니다 only if you wanted to have Breakfast but you were not able to have it since you were busy or for some other reasons. You would say '안' if you had time to have breakfast but you didn't have it on purpose. However we actually mix both 안 and 못. If it is confusing to you, you don't have to care about them so much.

I hope it helps :)

I correct my answer.

How would I answer this question?

Question: 아침 드셨습니까?
Answer: 네, 먹었습니다.

             아니요, (아직) 안(/못) 먹었습니다. -- Refer to Park's explanation.

             예. -- Many old Koreans say, "아침 드셨습니까?" instead of "안녕하십니까?"

                     So, we answer '예' whether we had breakfast or not.