  In this paper we find a third order unimodular matrix, none of whose entries
is $1$ or $-1$, such that when each entry of the matrix is replaced by its
cube, the resulting matrix is also unimodular. Further, we find third order
square integer matrices $(a_{ij})$, none of the integers $a_{ij}$ being $1$ or
$-1$, such that $\det{(a_{ij})}=k$ and $\det{(a_{ij}^3)}=k^3$, where $k$ is a
nonzero integer.
