Exercise 7, Appendix 2

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 that $\prod_{n=0}^\infty x_{\sigma(n)}$ is invertible. Now prove that each of the sequences $(x_{\sigma(n)})$ is multipliable (same reasoning as in prop. 9 of III, p. 44).