scissors are a big no no.. as it feels the same as cutting skin as cutting
the mat.

When my guys have matts, I do my best to break them up manually.  I take my
fingers and pull out a small piece of fur from one side.  Chopsticks help if
you don't have fingernails.  It is slow going, but it works for me.

I have 3 long haired cats. Boy do I have hair issues! I HAVE TO groom them
everyday. I use a fine tooth comb that is sold in the hair accessories
section of the store. The reason I use fine tooth combs that are sold for
human heads, is that they are cheap, easy to clean, and get at the undercoat
hairs. All cats have a top coat and an undercoat. Hairs shed at the root and
long-haired cats get hairballs more easily than short-haired cats because
they have longer hairs to groom. So, I suggest using hairball formula food,
maybe keeping hairball paste handy (comes in a tube like toothpaste and is
in the cat accessories section). Cats love hairball paste.

A cat hair brush only brushes the topcoat to make it look nice. A wire brush
will straighten and smooth out the hairs to keep the coat detangled. The
fine tooth comb I referred to will help comb out the shedded hairs from in
the coat. They do sell fine tooth cat combs but I think they are
ridiculously expensive when you can buy a human comb for $.39.

For matted hair, the only thing you can do is cut it off. Sorry, that's the
only solution I've ever been able to come up with. The best solution all
around is to prevent detangling to occur. You have to comb, and brush him
every day. If he's not used to the grooming, start out when he's calm and do
it in short intervals. Be consistent and eventually he will let you comb and
brush him all over. It may take a while, but be patient and don't push him
too far.

To cut the mats off, use blunt-end scissors if you have them, otherwise just
be careful. Try not to pull at the mat, it's a sore area because the hairs
being clumped like that already pull at the skin. Relieve some of the
tension of the mat by cutting into at several different angles first rather
than trying to cut it off right away at the skin. When one of my cats got a
mat of hair (gasp!!) in the groin area, I whittled away at it, cutting it
down from the tip of the mat till finally getting close to the skin and
could comb the rest of it out. He sure was protective of his groin area!
Imagine that! :)

If your cat is very apprehensive, just do a little cutting each day until
you finally get the whole thing. Try not to put him on his back if you can
avoid it, it makes him feel even more insecure. (Blunt-end scissors can come
in handy if a mat is under the cat and he won't let you turn him on his
back, then you can cut by feel using your hands and the blunt scissors and
never have to worry about poking him) It would be best to try a bit of
cutting when he's mellow and happy, maybe when you have him relaxed in a
petting session you can whip out the scissors and probably get away with a
snip or two before he realizes what you're doing. Don't let him see the
scissors coming if you can avoid it. If he gets scared, reassure him, talk
to him calmly and praise him ("good boy") if he lets you make progress with
him.  (Also pet and reassure him whenever you groom him so he learns it is a
positive experience to be groomed.)

It may take awhile, but you will get the matted fur eventually. Since he's
new he may be more nervous simply because he doesn't know you and is
generally unsure. It's new treatment for him and he doesn't know what to
make of it. So, be very pleasant, calm, and let him call the shots. If he
wants down and wants you to leave him alone, then do so. Matted hair isn't
an emergency, so you can take a little time with it. He needs to trust you
and learn that you're a good person. Lots of praise and petting (and
grooming!)!! Good luck!