Rescue cat dislikes being brushed???

[Red Rock]

To all cat people:

What suggestions do you have for a new cat (+/- month in new house). She does not like to be brushed. Basically, she runs away from you as you try to catch her to be brushed. Ms. Kitty as we call her, is a white persian. I have never owned a cat that did not like being brushed. How do I help change her behavior toward this.

Her current situation is that she has mats, and some severe ones on her back. Before we took her over, the person before us shaved off some of the really bad mats, so she is partly growing back new hair so skin is quite close.
We were thinking about taking her to be totally shaved, so she could "start off new". Would it be to soon to take to the groomers for this, or wait a little while longer?

I am attaching a picture so you might see what she looks like.

Thank you,
Red Rock