Should I put my screen protector on my iPhone 5 otterbox?

I just got my commuter otterbox case today and it came with a screen protector. But I don't know if I should put it on b/c I have two others cases. Should I put the screen protector on and keep it on even with my other cases? Or no?

Yes put it on carefully it will work with almost all cases and not only will it protect your screen from scratches it will prevent the little pieces of glass from falling out and poking you if your screen breaks