  The problem of when the vanishing of a (generalized) Schur complement of a
block matrix (corresponding to the leading principal subblock) implies that the
other (generalized) Schur complement (corresponding to the trailing principal
subblock) is zero, is revisited. A simple proof is presented. Absorption laws
for two important classes of generalized inverses are considered next.
Inheritance properties of the generalized Schur compements in relation to the
absorption laws are derived. Inheritance by the generalized principal pivot
transform is also studied.
