The correct answer is: A. “Hamlet” is going to be performed by them.
The other options are incorrect because they do not accurately reflect the meaning of the sentence.
Option B, “Hamlet” is going to perform by them, is incorrect because it implies that Hamlet is the one who is performing, rather than the people who are going to perform the play.
Option C, “Hamlet” is to perform, is incorrect because it implies that Hamlet is the one who is performing, rather than the play.
Option D, “Hamlet” has to be performed, is incorrect because it implies that Hamlet is the one who has to perform, rather than the play.
The sentence “They are going to perform “Hamlet”” means that the people who are going to perform the play are going to perform “Hamlet”. The play is the subject of the sentence, and the people who are going to perform it are the object. The verb “perform” is in the infinitive form, which indicates that it is a future action.