If the reader had any doubt of Claudius's role in the murder of Hamlet's father and plan to marry Hamlet's mother, there should no longer be any question due to the effects of The Murder of Gonzago, which Hamlet deftly gives a secondary name of The Mousetrap. The play-within-a-play clearly shows the original king and queen in love, the conspiring murderer poisoning that king, and the murderer then taking possession of both the crown and the queen. Note the exact lines from the text:
Ophelia. The King rises.
Hamlet. What, frighted with false fire?
Queen. How fares my lord?
Polonius. Give o'er the play.
King. Give me some light. Away!
This is an example of a time when it is definitely beneficial to be watching the play instead of reading it. Through the jumble of different voices here, the reader needs to ascertain that Claudius is so upset by what he sees on the stage (the mirror of his own actions) that he has to leave the room. During Hamlet's time, if the king rose and left the room in the middle of a performance due to ill-temper, the performance stopped. There is no exit without recognition. Everyone notices when the king leaves. This scene is no exception. And it is here, without any shadow of a doubt, that the reader can be sure that Claudius is guilty of his brother's murder, the insidious plan to gain the kingship, and the plan to marry Gertrude (Hamlet's mother). The question is, does this prove the ghost to be "honest"? Well, in one regard it does. Now we know that the ghost is "honest" in the sense that he was telling the truth about past events; however, what remains to be seen is if the ghost actually wants Hamlet's father to be avenged. You see, perhaps the ghost isn't "honest" at all. Perhaps what the ghost truly wants is for Hamlet to commit murder, die before forgiveness, and be damned to hell. Is the ghost committed to setting things right, or for Hamlet to join him in damnation? The answer to that question is for the reader (and many scholars) to determine.