  Recently there has been several works estimating the number of $n\times n$
matrices with elements from some finite sets $\mathcal X$ of arithmetic
interest and of a given determinant. Typically such results are compared with
the trivial upper bound $O(X^{n^2-1})$, where $X$ is the cardinality of
$\mathcal X$. Here we show that even for arbitrary sets $\mathcal X\subseteq
\mathbb R$,some recent results from additive combinatorics enable us to obtain
a stronger bound with a power saving.
