  We extend classical results on the classification of reversible elements of
the group $\mathrm{GL}(n, \mathbb{C})$ (and $\mathrm{GL}(n, \mathbb{R})$) to
$\mathrm{GL}(n, \mathbb{H})$ using an infinitesimal version of the classical
reversibility, namely adjoint reality in the Lie algebra set-up. We also
provide a new proof of such a classification for the general linear groups over
$\mathbb{R}$ and $\mathbb{C}$. Further, we classify the real adjoint orbits in
the Lie algebra $\mathfrak{gl}(n, \mathbb{D})$ for $ \mathbb{D}=\mathbb{R},
\mathbb{C}$ or $\mathbb{H} $.
