  This manuscript proposes a generalized inverse for a dual matrix called dual
Drazin generalized inverse (DDGI) which generalizes the notion of the dual
group generalized inverse (DGGI). Under certain necessary and sufficient
conditions, we establish the existence of the DDGI of a dual matrix of any
index. Thereafter, we show that the DDGI is unique (whenever exists). The DDGI
is then used to solve a linear dual system. We also establish reverse-order law
and forward-order law for a particular form of the DGGI, dual Moore-Penrose
generalized inverse (DMPGI), dual core generalized inverse (DCGI), and DDGI
under certain suitable conditions. Finally, the partial-orders based on DCGI
and DGGI are proposed.
