  Let $R$ be a Noetherian local ring and $m$ a positive integer. Let $I$ be the
ideal of $R$ generated by the maximal minors of an $m \times (m + 1)$ matrix
$M$ with entries in $R$. Assuming that the grade of the ideal generated by the
$k$-minors of $M$ is at least $m - k + 2$ for $1 \leq \forall k \leq m$, we
will study the associated primes of $I^n$ for $\forall n > 0$. Moreover, we
compute the saturation of $I^n$ for $1 \leq \forall n \leq m$ in the case where
$R$ is a Cohen-Macaulay ring and the entries of $M$ are powers of elements that
form an sop for $R$.
