  We show that the partial transpose of $9\times 9$ positive semidefinite
matrices do not have inertia (4,1,4) and (3,2,4). It solves an open problem in
"LINEAR AND MULTILINEAR ALGEBRA, Changchun Feng et al, 2022". We apply our
results to construct some inertia, as well as present the list of all possible
inertia of partial transpose of $12\times 12$ positive semidefinite matrices.
