Yes. All lawful permanent residents of the U.S. (Green Card holders) are required to have an eTA to fly to, or transit through, a Canadian airport. An eTA is valid for up to five (5) years or until the passport expires, whichever comes first.
You don’t need an eTA when you enter Canada by car, bus, train, or boat (including cruise ship).
You always need to carry your valid Green Card to show your status as a lawful permanent resident of the U.S.