According to one author, "Matrices over an arbitrary Boolean algebra β satisfy most of the properties over β0 = {0, 1}. The reason is that any Boolean algebra is a sub-Boolean algebra of β 0 S {\displaystyle \beta _{0}^{S}} for some set S, and we have an isomorphism from n × n matrices over β 0 S to β n S . {\displaystyle \beta _{0}^{S}\ {\text{to}}\ \beta _{n}^{S}.} "[1]