Is it wrong to log onto your ex's Facebook if you know something is fishy and found something out?

About six months ago, my boyfriend of about 2 years broke up with me. Two months ago, we started talking and planning on working things out and getting back together. We didn't have a label of boyfriend/girlfriend yet but we were waiting to go on a date; he said that labels don't matter (it is tricky because we live 4hrs away because of college). And some other stuff happened during the time we were trying to get together but I blew it off. After he visited over the weekend, the next day he decided to call it quits. He came up with "he just doesn't have time to put feelings into this, but he still wants to be friends and really close". It just sounded fishy and my gut was telling me, something was up. Usually my gut is right. I just felt used. I thought I might go onto his Facebook and see if there was anything suspicious. I know his password for his account because he told me it awhile ago. Once I logged into the account, I found out that he was asking girls out during the time that we were trying to get back together. He was also sending pictures of himself and receiving pictures of girls during the time that we were dating and talking about going down on a girl that he was messaging. I know what I did was not ideal, but do you think it is understandable? I mean, I found out proof that he was using me and cheating on me.
Is it wrong to log onto your ex's Facebook if you know something is fishy and found something out?
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