Aluminium metal is frequently used as a reducing agent for the extraction of metals such as chromium and manganese from their respective oxides, why?

Aluminium is more electropositive than Manganese($\mathrm{Mg}$) and Chromium($\mathrm{Cr}$). The process of reduction is known as Aluminothermy.

The Thermite mixture :

${\mathrm{Fe}}_2{\mathrm{O}}_3\left(\mathrm{s}\right)+\mathrm{Al}\left(\mathrm{s}\right)$ in 3 :1 ratio used

Reactions :

${\mathrm{CrO}}_3\left(\mathrm{s}\right)+2\mathrm{Al}\left(\mathrm{s}\right)\to {\mathrm{Al}}_2{\mathrm{O}}_3\left(\mathrm{s}\right)+\mathrm{Cr}\left(\mathrm{s}\right)$

$3{\mathrm{Mn}}_3{\mathrm{O}}_4\left(\mathrm{s}\right)+8\mathrm{Al}\left(\mathrm{s}\right)\to 4{\mathrm{Al}}_2{\mathrm{O}}_3\left(\mathrm{s}\right)+9\mathrm{Mn}\left(\mathrm{s}\right)$