An element a in a *-ring R has *-DMP inverse if there exists $m\in \mathbb{N}$ such that $a^m\in R^{\#}\cap R^{†}$ and ${(a^m)}^{\#}={(a^m)}^{†}.$ If m = 1, then a is said to have *-gMP inverse. In this paper, we present several new characterizations of *-DMP inverses in a *-ring. We prove that a has *-DMP inverse if and only if there exists a projection $e\in \mathit{comm}(a)$ such that $a+e\in R^{-1}$ and ae is nilpotent if and only if there exist $m\in \mathbb{N}$ and $x\in R$ such that $x{a}^{m+1}=a^m$ and $ax=xa={(ax)}^{*}.$ Moreover, we prove that $a\in R$ has *-gMP inverse if and only if $a{a}^{*}=ua,a^{*}a=av$ for some $u,v\in R^{-1}.$ The corresponding new characterization of *-DMP inverse is thereby obtained.

The paper focuses on the class of the Bott–Duffin inverses. Several original features of the class are identified and new properties are characterized. Some of the results available in the literature are recaptured in a more general form. BD matrices are also introduced and some properties are given.