A regular sequence is an $n$-fold collection $\{r_1, \cdots, r_n\} \subset R$ of elements of a ring $R$ such that for any $2 \leq i \leq n$, $r_i$ is not a zero divisor of the quotient ring $$ \frac R {\langle r_1, r_2, \cdots, r_{i-1} \rangle}.$$
Does the order of the $r_i$'s matter? That is, is any permutation of a regular sequence regular?