Answer
Person A is a knave, and person B is a knight.
Work Step by Step
Person A says "the two of us are both knights" and person B says "A is a knave."
If person B is a knight, person A must be a knave. If person B is a knave, person A must be a knight. Either way, persons A and B cannot both be knights. Because person A's statement is untrue, person A is a knave. Thus, person B is not lying and must be a knight.
