On some sets of permutation matrices

AbstractIn [5], a class Σ of p×p circulant matrices was studied where p is a prime, and necessary and sufficient conditions were presented for the matrices in Σ to be commutative and to be closed with respect to matrix multiplication. Here we show that these properties also hold for n×n circulant matrices, where n is a positive integer, with an additional condition, namely, Σ contains an n-cycle