On the basis of the paper [3]

this paper proved some characterizations ofthe reverse order law (ABC)+=C~+B~+A+ for the Moore-Penrose inverse relativeto an involutory function ρ of a matrix over a skew field

and obtained the corre-sponding characterizations of this law whose the term factors are an invertiblematrix

a projection matrix

a partial isometry matrix respectively over a p-di-vision ring

and also generalized the results of the papers [1] and E2] to a p-division ring.