*HAMLET* Was Gertrude in on it?

I always thought that Gertrude and Claudius were having an affair and planned to murder the king of Denmark(Hamlet's father) together. However my friend Celeste said that she didn't know anything about Claudius' plan to murder the king w/ ear poison and just married him after her husband's death to stay a queen. I still think she was in on it but, I'm curious as to what other people think? Thanks=)