If only one person is answering the question then the answer would be in singular and it would be "Yes, I am."
If it is asked to a group of people, then the answer would be in plural and it would be "Yes, we are."(The group may be a family or a group of tourists etc.)
Both are not correct but depending on the situation to whom the question is asked would the answer would be correct.
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SUDHKAMP
P.S. : I am not a teacher of English, but just someone who loves the language.

Student or Learner
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