From what I've read, there are many reasons why you would or wouldn't use il, la, nostri, etc. but it is optional if there isn't a noun after the possessive adjective, as in: la borsa è mia (no noun after mia, so no "la" needed), not la mia borsa (noun after mia, so the "la" is required).
The "la" can be used if you want to distinguish something or emphasize:
la borsa è mia = the bag is mine (describing the object)
la borsa è la mia = the bag is mine - out of many bags (describing possession/emphasis/distinction)
This can be shown by other adjectives as well:
la borsa è colorata = the bag is colorful
la borsa è la colorata = the bag is the colorful one