How does Dr Sullivan know A in Pretty Little Liars?

Answer 1

Because when Dr. Sullivan's office got broken into, on the wall in red written was 'nosey b**** must die' and as the girls know, it was A that broke in. After the girls tell Dr. Sullivan about A 'blackmailing' them she was reading through some ones file that goes to see her for therapy, and they referred to the girls as turning into 'nosey b****' after the death of Allison. Dr. Sullivan sees the link between that person and A, and therefore knows who A is. But because A has put a listening device in Dr. Sullivan's office, he/she knows that Dr. Sullivan knows his/her identity and is planning to tell the girls. Therefore to stop Dr. Sullivan reveling who A is, A kidnapped Dr. Sullivan.
A approaches Dr Sullivan and pays her off (I don't know if this is with money, or if A discovers something Dr Sullivan wants hidden, she then blackmails her).