이/가 is used at the end of a noun to express that the noun it accompanies plays the role of the subject of the sentence.
That being said, 이/가 can be used with any verb or the verb-like form of any adjective, and that, naturally, includes 이다.
[Examples with 이다]
- 내가 이 수업의 선생님이다. (I am the teacher of this class.)
- 이것이 내가 어제 잃어버린 축구공이다. (This is the soccer ball I lost last night.)
[Examples with other verbs]
- 의사가 수술을 집도했다. (The doctor performed the surgery.)
- 내가 갔다. (I went.)
[Examples with verb-like forms of adjectives]
- 그것보다 이것이 더 맛있다. (This tastes better than that. / This is more delicious than that.)
- 맥주가 차갑다. (The beer is cold.)
이/가 and 은/는 can be quite confusing for foreigners and some Koreans, but that's a seperate issue.
After reading your comments, I realized that I was confused as well. (Or, only I was.)
According to the dictionary, there are three usages of 이/가, and two of them are about using with nouns.
One is about marking the subject, and I already covered this. The other is about marking the complement.
- 나는 개구리가 되었다. (I became a frog.)
In this example, the frog is obviously not the subject, but it is the complement. 는 marked the subject 나(I).
You might ask: "If 이/가 can be used to mark both the subject and the complement, can they be used twice in a sentence?" Yes, they can.
- 올챙이가 개구리가 되었다. (The tadpole became a frog.)
If 이/가 is used twice in a sentence, the first one marks the subject and the last marks the complement.
As far as '이다' and '아니다' are concerned, I am not sure if it is about marking the subject or the complement. Personally I think it's about marking the subject, so I covered in my previous answer. Hope this helps.