TheParser's response is correct, but you asked for a reason, too. When you give a short answer to a question, you use the auxiliary, not the main verb. (We almost always use an auxiliary verb in questions; the most common one is "do.")
"Are you going to the party?"
"Yes, I am."
Long answer: "Yes, I am going to the party."
The main verb is "go;" the auxiliary verb is "be."
"Does she like pickles?"
"Yes, she does."
Long answer: [STRIKE]"Yes, I do like pickles/Yes, I like pickles."[/STRIKE] Oops, I meant, "Yes, she does like pickes/Yes, she likes pickles."
The main verb is "like;" the auxiliary verb is "do."
"Can they swim?"
"Yes, they can."
Long answer: "Yes, they can swim."
The main verb is "swim;" the auxiliary verb is "can."
"Have you read the book yet?"
"Yes, I have."
Long answer: "Yes, I have read the book."
The main verb is "read;" the auxiliary is "have."