"The bag is mine."
Translation:La borsa è la mia.
The meaning would be pretty close, but at this point there are certain grammar concepts we're trying to reinforce. Think of it like this: it is my bag and the bag is mine are slightly different, you wouldn't be able to say it is mine bag or the bag is my. In è la mia borsa and la borsa è la mia the pronoun and the adjective look the same, but they are two different parts of speech. È la mia borsa = adjective, La borsa è la mia = pronoun.
Yes, it was accepted for me, but I put it because a moment before I had read an answer that if you used the article before the noun, you did not need to use it again. Is this right or not?
Yep, nouns and adjectives must have the same gender.. So, it should be La borsa è (remember, it's with the accent) la mia.