The wave function of a many-electron

The wave function of a many-electron closed-shell atom can expressed as a Slater determinant (Section 10Ab). A useful property of determinants is that interchanging any two rows or columns changes their sign and therefore, if any two rows or columns are identical, then the determinant vanishes. Use this property to show that
(a) The wave function is ant symmetric under particle exchange
(b) No two electrons can occupy the same orbital with the same spin.

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