What major rivers that we have studied this year did alexander empire control

Tigris River, Nile River and Indus River.

When Alexander took the throne, he vowed to complete the plans of his father. After three grueling years of warfare, Alexander smashed the Persian armies at the Tigris River and conquered the Persian Empire. While fighting the Persians, Alexander conquered Egypt and founded a city at the mouth of the Nile River (Alexandria). He continued his campaign until he reached India and the Indus River. Where his exhausted troops refused to fight further. And without the support of his army, Alexander had to turn back and begin consolidating his empire.

He ruled an expansive empire.

yup! you are correct it is b.