My mom is in a care home and yesterday they shaved her face with a razor. I hadn't given permission. Can they do this?

The used a regular razor? Depending on the razor, they can be rough on skin. Like I posted, I bought a No No and kept it in my car. I had nothing at Moms NH that could be stolen.

I'm not sure what the problem is, what difference does it make? At mom's NH the ladies don't get a shave at all, if family doesn't do something about facial hair they just let it grow and frankly I would be pleased if I didn't have to do it.

You know, I do understand what you are saying. Speak to the supervisor, and let her know, what THEY di wrong, and show them what they are supposed to use.
Your brother probably didn't remember your instructions, or the one you had bought for them to use on her.
Just talk it out with them.
This was just an error. As long as they are taking care of her well, just have a nice talk with the supervisor.
Its stressful, I know and it has upset you.But your Mom, always wants to look nice, so the one time mistake will not effect her.
Good luck, and may God bless your Mom and your family.