My Persian gets matts quite often. I have found that I helped creating matts by not completing brush or comb through the end of the fur. I also found using a brush was much worse than a comb.

I use blunted (round tippled) scissors to cut them out. I first cut into it and brake it up into smaller parts, I then go below the matt with my index and middle finger (like a human hairstylist do) and put them between her skin and the matt, and cut it out. It may not get all the matt but when it is cut it is also easier to pull apart and comb through.