I searched a lot on internet, including here, but I couldn’t find an explanation that could convince me. The problem is the same of the title, if A is polynomial-time reducible to B and B is NP-complete, can I say that A is NP-complete too?

Actually, I would say yes, because if I can convert a problem that I don’t know how to solve to one that I know, then that problem must be at least as hard as the reducible one. So, A should be NPC.

However, I got to another idea that I can convert an easier problem to a hard one, so I could say that A is NP, but I couldn’t guarantee that it’s NPC.

Which ideia is correct?