Reverse order law for the core inverse of a product of two complex matrices

Abstract

In this paper,
necessary and sufficient conditions for the reverse order law $(AB)^{\co}=B^{\co}A^{\co}$ to hold are established.
In addition,
the hybrid reverse order laws $(AB)^{\dagger}=B^{\co}A^{\co}$ and $(AB)^{\#}=B^{\co}A^{\co}$ are also considered.