to Denmark's royalty by sacrificing herself in place of her son, a sacrifice she would quietly make until Laertes is struck with his own sword and cries out. Then, when Hamlet sees Gertrude and inquires how the queen is, the false Claudius says she is fainting over the sight of Laertes's and Hamlet's blood. The falseness of Claudius proves his treachery and his culpability for the murder of King Hamlet; this, then, forces Gertrude to warn Hamlet, "The drink! the drink! I am poisoned" (5.2.289) and she dies, hoping she has saved Hamlet and redeemed herself in her son's eyes.

When people die do they become privy to secrets that are unknown to all mortals? How much does the Ghost know about other things besides those he revealed to his son? Does the Ghost know whether or not Gertrude was involved in his assassination in any way? Is he able to listen in on their private conversations? Can the Ghost even listen to what is going on inside people's minds? The Ghost ought to know whether Gertrude is in any way guilty. When he tells his son Hamlet,

Let not the royal bed of Denmark beA couch for luxury and damned incest.But, howsoever thou pursuest this act,Taint not thy mind, nor let thy soul contriveAgainst thy mother aught. Leave her to heaven,And to those thorns that in her bosom lodgeTo prick and sting her....

the Ghost does not seem to believe that his widow has been guilty of murder or that she has any knowledge of what really happened. Since the Ghost is Hamlet's sole source of knowledge about his father's death, the Ghost also should be able to advise his son whether Gertrude was implicated in it as an accessory. But it seems apparent that Hamlet's father only holds his widow guilty of incest and perhaps adultery. He cautions Hamlet not to be too rough on his mother but to leave her to heaven. The Ghost wants violent revenge against his treacherous brother but not against his former queen. In fact, it seems as if he still loves her, which would not be the case if he suspected her of conspiring with Claudius in his murder--or even if he suspected her of carrying on an affair with Claudius while he himself was still alive.

Even Hamlet says to himself in Act III, Scene ii, while he is on his way to his mother's chambers:

I will speak daggers to her, but use none.

It would appear--from having the Ghost tell Hamlet to leave Gertrude to heaven and from Hamlet's telling himself that he has no desire to use violence against her--Shakespeare wants it to be clear to his audience that Gertrude is never in any danger when she starts crying for help and Polonius echoes those cries from behind the tapestry. It is a big misunderstanding. Hamlet has made everyone, including his mother, believe he is mad. Then when he goes to her chamber and they start to quarrel, he tells her:

Come, come, and sit you down. You shall not budge.You go not till I set you up a glassWhere you may see the inmost part of you.

He has no intention of being violent with her, but she thinks he is mad and takes his words literally--i.e., she thinks he is going to cut her open with his sword and set her in front of a mirror so that she can view her own intestines. Shakespeare had to establish that Hamlet was completely innocent of any such thoughts so that he will be taken completely surprise and will assume that he has walked into a trap. Hamlet still suspects Gertrude of being implicated in his father's death, and he thinks it is Claudius rather than Polonius who is hiding behind the tapestry. He suspects that Claudius and Gertrude, who were co-conspirators in his father's assassination, have now conspired to trap him and have him imprisoned or executed for attempting to kill the Queen. 

When Hamlet asks his mother how she likes the play, she replies, "The lady doth protest too much, methinks." Obviously she is focusing on the Player Queen and identifying with the lady. Gertrude is unaware that she is revealing something about her own character. She takes it for granted that the Player Queen is exaggerating outrageously when she tells her husband how utterly impossible it would be for her to marry another man if her husband were to die. Gertrude knows that most women lie to their husbands, and that the Player Queen is only telling the Player King what he wants to hear. By saying that the Player Queen is protesting "too much," Gertrude means that she is not doing a good job of lying. Less is more. It would be more effective for the Player Queen to say something much briefer and simpler, such as, "Don't even talk about it! If you died I would want to die too." Gertrude assumes that other women would remarry if they lost their first husbands, because marriage was about the only option women had for sheer survival. 

What probably happened was that Claudius killed his brother, as the Ghost describes the event, and proposed to Gertrude shortly thereafter. He was making her an offer she couldn't  refuse. If she didn't marry him, he was bound to marry somebody else. No doubt he would marry a younger woman and she would have children. Gertrude would be in the position of a poor relation, and her son Hamlet would never have a chance at the throne. They might even be lodged in some other domicile and forgotten. If the new queen had a child, he or she would be first in line of succession. At that point, Claudius might decide to dispose of Hamlet in order to forestall any controversy over the crown after his own death. 

Claudius was king of a powerful country. He could have had his choice of brides from royal houses all over Europe. But he might have been tempted to propose to the luscious young Ophelia--and she would have accepted because she would do what her father ordered her to do--and Polonius would like nothing better than to have his daughter made queen.

Gertrude may not have been motivated by love or lust at all when she married Claudius. That was Hamlet's interpretation of her motivation and subsequent behavior. Gertrude may have only been responding appropriately to Claudius's love and lust. As Hamlet observes:

You cannot call it love; for at your ageThe heyday in the blood is tame, it's humble,(75)And waits upon the judgment; and what judgmentWould step from this to this? - See more at: http://www.enotes.com/topics/hamlet/etext/act-iii#etext-act-iii-act-iii-scene-iv

Assuming Gertrude was not an accessory in her husband's murder, would she have married Claudius if she knew or even suspected that he was the murderer of her first husband? 

Many literary critics strongly believe that there are enough evidences that support Gertrude’s crime. Atwood has supported this view strongly in Gertrude Talks Back. In this work, Gertrude tells why she disliked Old Hamlet as well as what qualities in Claudius made her get attracted to him:

But handsome isn't everything, especially in a man, and far be it from me to speak ill of the dead, but I think it’s about time I pointed out to you that your dad just wasn't a whole lot of fun.

But Claudius, well, he likes a drink now and then. He appreciates a decent meal. He enjoys a laugh, know what I mean? 

In the end, Gertrude leaves no room for doubt. 

It wasn't Claudius, darling. It was me.

But weather Gertrude had a role in Old Hamlet’s murder in Shakespeare's Hamlet remains uncertain and ambiguous. First of all, we don’t see Gertrude making any clear statement that makes her guilty of the crime, but of course, there are certain elements in the play that make her a shadowy character.

For example, not for once do we find her really mourning her husband’s death, which is pretty unusual and even cruel. She takes no time in coming out of such an earth-shattering grief. There’s also a lot of rush and haste in her marriage with her husband’s brother, i.e. Claudius. Besides, she ardently supports Claudius and takes his side. Many critics claim that Gertrude loved Claudius even before Old Hamlet died. Although all this adds fuel to our suspicion, it doesn’t clearly make her the murderer. From this, we can just blame Gertrude of incest and adultery. Gertrude tries to force Hamlet to forget his dead father and move on. Again, this could be because she wants Hamlet’s happiness. For sure, she loves Hamlet very much. As a wife and queen, however, her behaviour is absurd.

We don’t find Gertrude thinking about the murder in private and she never confesses her sins. It is mainly through Hamlet’s thoughts about Gertrude that we try to analyse her character and deeds. Hamlet considers Gertrude’s marriage to Claudius as a shameful act driven by lust. Her desire to be with Claudius could be a reason for her to take her husband’s life. Again, we cannot be sure about this. In Act 3 Scene 4, we notice that when Hamlet accuses her of Old Hamlet’s murder, she reacts with complete shock and surprise.

What have I done, that you dare scream at me So loudly and rudely?

Note that the Ghost of Old Hamlet also doesn’t accuse Gertrude of the murder and stops Hamlet from hurting her mother. The Ghost claims that it is all Claudius' fault and even calls Gertrude virtuous.

The will of my most seeming-virtuous queen

Apart from this, Gertrude doesn’t do any other cunning acts in the entire play. Looking at things from this perspective, we might think that Gertrude didn’t murder the Old Hamlet. But, of course, nothing is conclusive.

Combined with Atwood's depiction, Gertrude speaks in a complex manner where she can be seen as being "in the know" about what has happened in the Denmark monarchy.  Gertrude initially calls to see Hamlet in a complex manner.  Polonius is behind the curtain and she speaks with Polonius in a manner that reflects some level of intricacy:  "I'll warrant you; Fear me not. Withdraw; I hear him coming." This indicates that Gertrude does not call for Hamlet in the transparent and innocent manner of a mother calling for a child.  When she accuses Hamlet of offending his father, the bitter exchange begins. Hamlet's accusations evoke responses that reflect complexity and, perhaps, duplicity.  One example of this would be when she says that Hamlet speaks with an "idle tongue" and questions how Hamlet can speak to her in such a manner.  Gertrude might be speaking from a position of the offended mother or simply deflecting accusation and blame.  

As the scene progresses, Gertrude begins to speak as if she recognizes that the situation is growing out of her control. When Hamlet threatens to expose via mirror what Gertrude as done, her response reflects complexity: "What wilt thou do? Thou wilt not murder me? Help, help, ho!"   It is at this point where Gertrude can be seen as being "in the know."  Atwood assumes this position in articulating how Gertrude not only was "in the know," but justified in what she did.  

But handsome isn't everything, especially in a man, and far be it from me to speak ill of the dead, but I think it’s about time I pointed out to you that your dad just wasn't a whole lot of fun. Noble. Sure, I grant you.  But Claudius, well, he likes a drink now and then. He appreciates a decent meal. He enjoys a laugh, know what I mean? You don't always have to be tiptoeing around because of some holier-than-thou principle or something.

In both moments, it becomes clear that Gertrude was "in the know" because of what she endured as the King's wife.  She possesses multiple dimensions as wife, mother, and woman who had endured consciousness in silence.

Gertrude becomes complex because she seeks to have her voice heard, her experience as the Queen validated. When the mother asks her son, "What have I done, that thou darest wag thy tongueIn noise so rude against me," it is a moment in which Gertrude can be seen as rhetorically justifying her actions.  It is akin to asking if Hamlet can comprehend what her life has been like, as if what has been done could not be understood on the son's part. Atwood clearly indicates this:  "You have no idea what I used to put up with. And every time I felt like a little, you know, just to warm up my aging bones, it was like I'd suggested murder."  This complexity compels her tell Hamlet not to speak to her anymore and to simply go. When Gertrude says to Hamlet, "thou hast cleft my heart in twain," it could be reflective of her guilt being exposed or the emotional cruelty of a son failing to understand his mother.  This is also seen in her wondering what should be done at the end of the scene, reflective of even more complexity in her characterization. It is here in which one can see her as being "in the know," something that Shakespeare intimates and Atwood clearly states. Such divergence is where the richness of her characterization lies.

It isn't clear how involved Gertrude is in the murder of her first husband. She marries Claudius only a few months after the king is murdered, but the Ghost of Hamlet's father tells Hamlet not to harm her. Wouldn't King Hamlet's want revenge on her as well if she had been a part of it? She is dependent on Claudius and is easily manipulated by him, so she could be easily fooled by him. In Act I, the Ghost denounces Claudius for seducing Gertrude. Critics disagree whether this means Gertrude was having an affair before the king's death, or if the Ghost was referring to their marriage after his death. By the final scene, Gertrude seems to suggest that she was unaware of the crime. This is one of those questions where you could make an argument either for or against Gertrude's involvement.