  For a prime power $q$, we study the distribution of determinent of matrices
with restricted entries over a finite field $\mathbbm{F}_q$ of $q$ elements.
More precisely, let $N_d (\mathcal{A}; t)$ be the number of $d \times d$
matrices with entries in $\mathcal{A}$ having determinant $t$. We show that \[
N_d (\mathcal{A}; t) = (1 + o (1)) \frac{|\mathcal{A}|^{d^2}}{q}, \] if
$|\mathcal{A}| = \omega(q^{\frac{d}{2d-1}})$, $d\geqslant 4$. When $q$ is a
prime and $\mathcal{A}$ is a symmetric interval $[-H,H]$, we get the same
result for $d\geqslant 3$. This improves a result of Ahmadi and Shparlinski
(2007).
