  In this paper, we introduce new representation and characterization of the
weighted core inverse of matrices. Several properties of these inverses and
their interconnections with other generalized inverses are also explored.
Through one-sided core and dual-core inverses, we have shown the existence of a
generalized weighted Moore-Penrose inverse of matrices. Further, by applying a
new representation and using the properties of the weighted core inverse of a
matrix, we discuss some new results related to the reverse order law for these
inverses.
