そうです or そうでした for sentences that end with でしたか

Question

山下先生のせんこうはれきしでしたか。

To answer the above sentence, would the sentences below be acceptable?

1. はい、そうでした。
2. はい、そうです。

Is 1 the only acceptable answer since the question is in past tense?

Answer 1

Both are possible, and the choice will depend on the context and the mood. (Why is the first question in the past tense?) If you are objectively saying "Yes (that is right)", そうです is the natural choice. But そうでした is also fine in the following situations:

• When you are vividly recalling him at some point in the past (e.g., he is already a dead person and you remember the lecture he gave to you)
• When you want to somehow emphasize his current major is no longer history
• When the question reminded you of that fact (modal-た)

Answer 2

I would say

はい、そうです。

because it means Yes, that is correct. Answering with はい、そうでした may be ok but it sounds a bit strange to me as it sounds like Yes, that was correct.

Other answers I may hear people say would be

はい、れきしでした

はい、れきしです