In my opinion I think that Gertrude does know about Claudius killing his 

brother. The thing the drew me most to this conclusion was that Gertrude does 

not even seem to care that her husband, who she was with for many years, has 

died. Not once does she even mention that she is sad about it, she immediately 

moved on. I know from personal experiences that people can take years to get 

over a person, more than just merely two months to move on. Also it is very 

uncommon to, not only feel little to no emotion about the death of a loves one, 

but also to remarry that quick. Keep in mind that King Hamlet and Gertrude had 

been married for many years, over a decade. Being married for that long you 

would think that the two would have build a strong emotional bond between

them. If she was not in on Hamlets murder then she would be devastated by her

husbands death but as we see that is clearly not the case. Another thing is that

when prince Hamlet is talking to the king and queen, Gertrude tells him "Thou

know'st 'tis common: all that lives must die, Passing through nature to eternity." 

(1,2,74-75) Gertrude's words are the most common thing to say to someone who

is mourning a loved one, she says nothing with real meaning, she does not even

make any reference to how she had to deal with this sadness as well but now

she is over it. I think it is because she never felt any sadness to begin with,

which would only make sense if she had already known about Claudius

murdering King Hamlet.

     Another thing that made me question Gertrude's innocence is who she chose

to remarry to. I think that it is strange that very shortly after her husband dies 

she gets married to her husband's brother. In my opinion if I was to get 

remarried to someone else I would not get married to my spouses sister. If I

were committed to get into a new relationship, in a sense starting a new life with

a new person, I would marry someone who would not be a living reminder of the 

person I just lost. I would want to get on with my life and forget the past but 

if I were to marry someone related to the deceased then that would be nearly 

impossible. Also it seemed a little weird to me that right after King Hamlet 

dies Gertrude marries Claudius. To me it seemed planed, it was two months

before they got married which is long enough to convince people that Gertrude

could get over King Hamlet in that time, and it is just short enough to seem as if

the action was rushed. Prince Hamlet himself thinks that the marriage happened

to fast "Thrift, thrift, Horatio. The funeral baked meats did coldly furnish forth 

the marriage tables." (1,2,184-185) Overall that is why whole ordeal seems 

suspicious to me and why I think that Gertrude knew about Claudius murdering 

king Hamlet.