  The notion of the core inverse of tensors with the Einstein product was
introduced, very recently. This paper we establish some sufficient and
necessary conditions for reverse-order law of this inverse. Further, we present
new results related to the mixed-type reverse-order law for core inverse. In
addition to these, we discuss core inverse solutions of multilinear systems of
tensors via the Einstein product. The prowess of the inverse is demonstrated
for solving the Poisson problem in the multilinear system framework.
