reciprocal power GCD matrix and reciprocal power LCM matrix defined

on a set $S$ consisting of three quasi-coprime divisor chains with

$\gcd (S)\in S$. Consequently, it was showed that the reciprocal

power GCD matrix and the reciprocal power LCM matrix defined on $S$

with $\gcd (S)\in S$ are nonsingular. But such result is not true

when $S$ consists of three divisor chains which are not

quasi-coprime.