Edited sentence: A less trivial example is the set Matn(B) of square matrices over a boolean algebra B, where the matrices are ordered pointwise.For example, every ordered group is residuated, and the division defined by the above coincides with notion of division in a group.It can be shown that X\Y = (YtX’)’ and X/Y = (X’Yt)’, where (X’ is the complement of X, and Yt is the transposed matrix).Matrix multiplication is defined in the usual manner with the "product" being a meet, and the "sum" a join.The pointwise order endows Matn(B) with pointwise meets, joins and complements