Can my cell phone company track my location if I turn off gps?

My iPhone had a GPS which can find nearest places. If I turn it off, will my T-Mobile company see my location if authorities ask.

Yep

Of course, your gps is only for navigation for the user or weather apps, your location is determined by the towers, latitude and longitude, so when you call, text, play an online game that's telling pretty much everyone where your located… Even I feel you don't use your phone for those things and use it for offline games, intelligent agencies such as the nsa or fbi can still echo request your phone and determine its exact location, they're even liable to turn on your gps internally while it looks off to the user

Yes.
The mobile phone system inherently "knows" the distance between the phone and the cell towers it is in range of.

It is a fundamental part of the system, that allows it to compensate time slot drift due to propagation delays and to select which cell to use for the main connection to the phone at any instant.

Not only Apple tracks your phone but many apps as well.

Don't worry.

It is virtually impossible to go Anywhere these days without someone knowing Exactly where you are.

By other means, yes.

Yes, any sellphone company can track your location.

Yes. GPS is only a useful tool for you to use with apps such as navigation. I don't know why app makers feel there's a need for them to have access to your contacts files, media etc. I don't give blanket approval to those apps to do as they wish, so I find them unfunctional and delete them. Google is a bit of a concern too, constantly asking me to make comments on places I have visited in the past. My phone must have a life of it's own though… As I'm ask to write comments on places I have never visited!

Yes, there's is an option.