I'm going to look at my ex-girlfriend's facebook when I suspected she cheated
Are you sure she cheated on you?
No, I just suspected it and I didn't know which thoughts to believe.
It's not very wise to continue to loom over an ended relationship, it can be unhealthy for your mental state. Sometimes it pays to just disconnect from social media and work on yourself.
I want to know the reason why she broke up with me
It is ok to want to know why you broke up, but going on her Facebook like that is not the way. Just ask her, and if she does not tell you, leave the situation alone and move on.