I removed our ceiling light today and the house wiring had no distinction between the two wires connecting to our light. The light fixture's wire had the same color insulation, but inside, one of the wires had red metal/copper and the other had silver metal. I assumed that the silver metal wire was therefore connected to the neutral house wire and so assumed the house wire on the right was neutral. Again, the house wires were identical, AFAIK.
Then, our new light had two similar wires as well, although the insulation on one of them had white writing, which I assumed should be connected to the neutral house wire.
Questions: 1) Am I correct in what I assumed and did? 2) I have a cheap multimeter with red and black leads. Can I use this on the live circuit to confirm which is which? I tried using my multimeter in an outlet, and both ways I tested the two-pronged outlet (red on left, black on right and vice-versa) gave me the same 120v reading - neither flipped the direction of the meter, so hopefully there is another way to do this. My meter looks like this: https://goo.gl/images/9eF4KP