Exercise 7, Appendix 0

Let $(x_n)$ be a sequence of points of a normed algebra $A$, such that for every permutation $\sigma$ of $\mathbf{N}$, the infinite product with general factor $x_{\sigma(n)}$ is convergent and $\prod_{n=0}^\infty x_{\sigma(n)}$ is a unit. Show that each of the sequences $(x_{\sigma(n)})$ is multipliable (same argument as in Chapter III, § 5, no. 7, Proposition 9).