Should you trust someone after they’ve shown you their true colors?

I’ve been having problems with this girl giving me backhand compliments and just being super self centered (we’re in the same coed fraternity). We got into an argument (we were both in the wrong) and she accused me of doing something (it was later found out that I didn’t do what she accused me of) and threatened to tell the university in hopes of me losing my scholarship. We had to talk to the exec board of our fraternity, and she while I apologized, she refused to admit that she was wrong and refused to apologize. A few months go by, and she’s talking to me like we’re friends and like nothing happened. I just don’t think I can trust her though.

I was friends with another girl (in the same frat) and I told her something personal, and she told the girl I mentioned above, and that girl used it against me. I talked to my friend about it, because she knows that the other girl does not like me, and she said that she was just causally talking to her and didn’t think that she’ll use what I told her against me. I don’t know if I should trust her either.
Should you trust someone after they’ve shown you their true colors?
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