You need to carry your passport for age verification.
Original passport, for sure, will be an undeniable proof. A photocopy officially is not a proof at all, but may be accepted if the person in the booth is in the kind mood.
I've never carried my passport around with me. I carry a photocopy and it has always been accepted as proof of my age.
Mind you, maybe the grey hair is a give away!
It's mostly your good looks and a smile.