Consider $G=GL(n,q)$. A regular semisimple element of this group, is a matrix, whose characterestic polynomial is square-free and same as minimal polynomial. Results show that the number of such matrices in $G$ is a polynomial in $q$, with degree $n^2$, and coefficient of the leading term being 1.

Does similar hold, when we take $G=SL(n,q)$, that is, the number of such matrices in $G$ is given by a polynomial in $q$ of degree $n^2-1$, with the leading term being 1?

I appreciate any kind of help or references that can be of use. Thank you.

elements, but the number of rssclassesis well studied. I'm familiar with Steinberg (see, for example, §14 of Steinberg - Endomorphisms of linear algebraic groups); but some Googling also turned up Fleischmann, Janisczczak, and Knörr - The number of regular semisimple classes of special linear and unitary groups. $\endgroup$ – LSpice Apr 16 at 1:27