Q. Tan [Linear Multilinear Algebra 58, No. 5-6, 659–671 (2010; Zbl 1245.11037)] proved that if \(S\) consists of two coprime divisor chains and \(1\in S\), and if \(a|b\), then the power GCD matrix \((S^{a})\) divides the power GCD matrix \((S^{b})\) in the ring \(M_{h}(\mathbb{Z})\) of \(h \times h\) matrices over integers. Similar results for power LCM matrices and mixed cases were also obtained. In this paper, the authors treat the remanning case of \(1\not\in S\).