the question was: prove that if intersection of NPC and co-NP is not empty, then NP=co-NP.

I didn't understand a few things:

1. If there's a polynomial mapping reduction from A to L, then we said that there's a polynomial mapping reduction from A comp to L comp.

Why is that? I can understand why there is a mapping reduction but why is it polynomial?

2. In the second direction we said that A comp is in NP and therefore A comp is in co-NP. why?

thanks