Pauli Exclusion Principle

Cannot have two identical fermions in the same state.

So if we have $|{\mathrm{\Psi }}_1⟩=|ab⟩$ and $|{\mathrm{\Psi }}_2⟩=|ba⟩$. Then for identical bosons, we have $|{\mathrm{\Psi }}_S⟩=\frac{1}{\sqrt{2}}(|{\mathrm{\Psi }}_1⟩+|{\mathrm{\Psi }}_2⟩)$. Then for identical fermions, we have $|{\mathrm{\Psi }}_A⟩=\frac{1}{\sqrt{2}}(|{\mathrm{\Psi }}_1⟩-|{\mathrm{\Psi }}_2⟩)$.

So if $a=b$ then the fermionic wavefunction is zero.