Gertrude’s behavior and her words proved that she had no clue Claudius had murdered the Old king. In Act 1, scene 5, Hamlet learned the truth from the ghost that his father was killed by Claudius. This ghost said that “The serpent that did sting thy father’s life
Now wears his crown.” It basically indicates that Claudius was the person who killed him. Nevertheless, the ghost never mentioned that Gertrude was involved in this crime. It also did not want Hamlet to take a physical revenge upon her, but make her suffer from the guilty for the rest of the life. The reason the ghost criticize her was not because of the murder, but the incestuous thing she has done, betraying himself and married Claudius in such a brief time. Also, Gertrude seemed to still care about Hamlet a lot and treat him pretty as a normal mother would do. It would be particularly surprising if she then, apparently genuinely, worried and wondered over Hamlet’s behaviour, wanting him to stay with her at court and hoping that he would look positively on his uncle: ‘let thine eyes look like a friend on Denmark’; ‘let not thy mother lose her prayers.. I pray thee stay with us ...’
Gertrude, herself, gives no soliloquies of guilt and, in the lines that she speaks, gives no indication of having been involved in the murder. If she and Claudius had planned the killing together, then one might expect that they would discuss the matter, or, at least, allude to it, in their private conversations, but they do not. She comments, in act 2, scene 2, that the cause of Hamlet’s ‘distemper’ is likely to be ‘his father’s dath and our o’er-hasty marriage.’ She seems to have no idea ~ and no reason to think ~ that Hamlet believes that either of them is guilty of his father’s murder.
When Hamlet set up the dumb play and tried to observe Claudius’s reaction, Claudius showed extremely frustrated and upset as watching the show, which was referring to his own crime. But