if A were clever, A might have been promoted to a manager.
I think you had better get a written confirmation on everything A asks you to do just in case. A may not know how to protect his/her team's interest (or even his/her own interest). For this reason, it is important for you to take care of your own interest, not to become a scapegoat.
If you only plan to stay there for a short time, then review/rewrite your CV on a regular basis, focusing on how/what to translate whatever you do to your CV. In addtion, I don't usually recommend this, in this situation it is what you do is important, not how well you do.
