A new class of rectangular zero prime multivariate polynomial matrices are introduced and their inverses are computed. These matrices are ideal for use in multidimensional systems involving input-output transformations. We show that certain multivariate polynomial matrices, when transformed to the sequence space domain, have an invertible subsequence map between their input and output sequences. This invertible subsequence map can be used to derive the polynomial inverse matrix together with a set of pseudo-inverses. All computations are performed using elementary operations on the ground field without using any polynomial operations.