Partial transpose of a maximally entangled projector ($(|{\Phi }_d⟩⟨{\Phi }_d|{)}^{T_B}=S/d$)

For $|{\Phi }_d⟩=d^{-1/2}{\sum }_j|jj⟩$, the partial transpose of its pure state projector is $S/d$, where $S$ is the swap operator. Expand in matrix units: $|i⟩⟨j|\otimes |i⟩⟨j|$ becomes $|i⟩⟨j|\otimes |j⟩⟨i|$.