You sure can. As long as you don't expect answers, you can ask him anything you want. Shucks, you can ask him what he was thinking that one time when he did that thing that he did while you were doing that thing that you do when you all had did what you didn't do.
Dum dum didday.
I realize that you're probably a woman. And women like closure. Actually, I suppose men do to. Anybody who got their heart caught in a blender probably wants to know what happened. But you do have to realize, that for a lot of people, once they breakup with you or move on, they don't feel like they owe you anything or have any desire to rehash the painful memories (or douchebag memories) that led to your breakup. So while I understand the desire to ask what happened, just realize that he might not feel inclined to answer nor does he want to discuss your relationship at all. It would be nice if he gave you some inkling, but you also have to ask yourself this:
Are you asking just for personal information reasons, or are you hoping to attempt to address whatever it is so that you two can get back together?
If your ex wanted to be back with you, he'd probably let you know. If he hasn't, then he's probably good on being single again.
So ask away; hit him with your best shot. Just be prepared to get nothing in return.
It was written.