You need to snip the mats off because they will usually be too thick, tight to the skin, or tangled to pull apart or brush/comb out. From now on this is your responsibility. You need to comb her back, which is something kitties usually LOVE. Brushes are cheap--buy one for a cat that is well made and will last, one that doesn't have bare metal bristles.
Even if you don't have a Persian or cat with full long hair, a cat with mats can harbor a lot of dander, provide a haven for fleas, smell, and even get hot spots. The finer the hair the more dangerous it is to get the mats off. With most super-fine haired Persians you have to use a shaver and blunt-edged nursing scissors--that's how bad it is. You probably don't have nearly anything like those challenges on your hands.
Once you clip those mats, you might consider giving her a bath if it's not too cold where you live. That can release a lot of grit from litter, a lot of dandruff, eggs, dander, etc. Then towel dry as much as possible. If she'll tolerate a blow dryer on low heat and a good brush as you do it, that would be what groomers do with their purebreed show cats. You'll have to brush her out fully, and comb everywhere, once she's fully dry.