Centralizing maps on invertible or singular matrices over division rings

Let D be a division ring and let Mn(D) be the ring of all n×n matrices over D with center Z, where n⩾2 is an integer. We describe the additive map f:Mn(D)→Mn(D) such that f(x)x−xf(x)∈Z for all invertible (singular) x∈Mn(D).