  Let $A$ be a set in a prime field $\mathbb{F}_p$. In this paper, we prove
that $d\times d$ matrices with entries in $A$ determine almost
$|A|^{3+\frac{1}{45}}$ distinct determinants and almost $|A|^{2-\frac{1}{6}}$
distinct permanents when $|A|$ is small enough.
