The invariant factors of the incidence matrices of points and subspaces in PG(n,q) and AG(n,q)

We determine the Smith normal forms of the incidence matrices of points and projective (r-1)-dimensional subspaces of PG(n,q) and of the incidence matrices of points and r-dimensional affine subspaces of AG(n,q) for all n, r, and arbitrary prime power q.