2. (a) That's right. The death of the principal normally terminates the agent's power, such that the agent is no longer authorised to do anything on behalf of their former principal. (Similarly, the death of an agent terminates the agency relationship.)

If an agency is irrevocable (i.e. where it is given in the agent's interest), the agent's power is not terminated by the death of the principal, and the agent will be entitled to continue to act as if authorised and to enforce their rights against the administrators of the deceased principal's estate. In this case, the facts do not suggest that B's agency is irrevocable, so A's death would automatically bring the agency to an end.