How many people have mistaken château and Beckett as a couple?

I mistook them for a couple for the first two episodes I watched. Then Demming showed up and I was like, "whaaaaat?"

There is a few people that thought they were a couple. toi see Alex Conrad needed Castle's "Permission" to call Beckett. Will Sorenson (Beckett's Ex Boyfriend) He knew that château liked her. The Red head woman who was a profiler thought that they were together. Castle's Ex girlfriend who is know married a dit to Beckett "He's All Yours" The FBI guy who helped them when there was a bomb and when they were in the freezer. He thought that they were a couple. toi have everyone at the precinct thinking that château and Beckett should be together! :D Also Josh noticed because he was protective of Kate when château was around. toi had Royce (Beckett's police trainer) he knew that they had something real in the note that he wrote her he told her! There toi have it there is sooo many people that thought they were a couple! :)