Lighting, Light Fixtures, Ceiling and Exhaust Fans - Replacing ceiling light in older home

I was recently trying to replace a ceiling light fixture in my older home for the first time. When I took the original hanging fixture down, it only had 2 wires (no color codes) and the two house wires looked the same. I decided to hook it up to the new fixture without knowing which house wire was hot. Everything works fine, but now I'm worried about it. Is there any way of checking if I did it right without taking it down again? Would it have worked if I had done it wrong? If so, is it dangerous?
Thanks!

Yes hooking them up backwards can be dangerous. The hot could get connected to the frame of the light, not a good thing. I assume by old you mean more than 60-70 yrs. Fabric covered wires, that appear brown?? Look more closely, one of this coverings has some white threads in it, that should be neutral.

Depending on the type of light it may have a requirement to be used with 90 degree Celcius wiring. Pre 1987 wiring will not meet this and could cause afire.