Questions & Answers about Мой дедушка был для меня авторитетом.
Авторитетом is in the instrumental case.
In Russian, when you say that the subject was / became / is something like a profession, role, or status, the noun after быть (to be) is usually in the instrumental:
- Мой дедушка был авторитетом. – My grandfather was an authority (figure).
- Она была учителем. – She was a teacher.
- Он стал врачом. – He became a doctor.
So авторитет → авторитетом (masculine singular instrumental).
The form авторитет (nominative) would be ungrammatical in this sentence.