Answer
Hamlet knows exactly who she is her husband's brother's wife and unfortunately his mother. Gertrude tries to convince Hamlet but she cannot get through to him past the hatred he feels towards her for marrying her brother-in-law so quickly after her husband's death
Gertrude is Hamlet's mother and she is the Queen of Denmark. Her relationship with Hamlet is somewhat unstable since he holds a grudge against her marrying her husband's brother Claudius after he killed the king.Hamlet's father King Hamlet
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