It's a question us cat-lovers often ask ourselves - how and when should I groom my cat's coat? For the most part, cats are expert groomers themselves - and they have some great built-in tools. That raspy tongue 'rakes' over their coat eliminating shedding fur. Their saliva is their version of a bath wash, cleaning as they go. Back claws are great for detangling like a wide tooth comb. And that cute display of licking their paw after a meal is just like using a soft wash cloth to clean their face.
But even with this fastidious hygiene, cats benefit greatly from daily brushings to help simplify their job, especially during heavy shedding season in the spring and fall when their coat thins/thickens for the change in weather. Indoor cats will shed as well, essentially year-round due to the artificial light they receive daily. So remember to spend some quality time brushing your cat as it will comfort them and help them bond to you, their 'human mother'!
Now when it comes to mats, that's an entirely different situation, and can be a serious one if not dealt with quickly. Besides being tangled fur, mats consist of dead skin and oils that form that hard pelt-like clump. Senior and overweight cats, who may have trouble reaching their entire body, are especially susceptible to matting. Long-hair cats typically have more problems with mats than short-hair cats, but short-hair cats are not free from the condition. You'll notice mats are more likely to form in the tummy and hind end flanks, also on their chest and under front legs.
Besides looking unruly, mats can become painful as they solidify and stretch your cats thin, sensitive skin. So brushing will ideally keep this under control, but when mats form, it's important to groom your cat to remove them. Metal combs with straight smooth tines are the tool of choice. Bristle or pin brushes may feel good to your cat, but are quite ineffective for detangling. Working gently with slow stokes is best. DON'T tug -- imagine gum stuck in your hair, no-one wants that to be pulled at! Scissors should be used very sparingly to avoid cutting skin. Mats close to the skin are hard to differentiate. If you have to cut out a mat, slide your comb in and cut only above the tines. There may be some situations where a professional is needed, so don't take on more than you can handle in a particularly bad case.
Shaving should be a last resort in severe instances of matting and left to a professional. The cats coat, even a long hair one, is vital to regulating a cat's temperature and can actually cool a cat in summer. It can block UV rays and allow for air-flow, so never think of shaving as a way to cool at cat down.
So the answer is yes - grooming your cat is a good idea, as long as it's done correctly. Your cat will likely let you know when she's ready for that brush!