The two conclusions that this excerpt best supports are:
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Caesar and his wife do not have children. - This is implied in the mention of Calpurnia being barren ("the barren, touchèd in this holy chase"), which suggests they have not had children.
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Antony does whatever Caesar says. - This is supported by Antony's response to Caesar, "When Caesar says 'do this,' it is performed," indicating his loyalty and obedience to Caesar's commands.