Complexity of solving linear equations
I’m not sure this is a research-level question, however solving linear systems over $\mathbb F_p$ is a $\mathrm{Mod}_p\mathrm L$-complete problem, hence in particular it is in $\mathrm{NC}^2$. More generally, linear algebra over $\mathbb F_{p^k}$ (at least for $k$ fixed) can be reduced to the $\mathbb F_p$ case.