On the determinants of divisor matrices (Q1874374)

Divisor matrices \(A_n\) are special \((0,1)\) matrices defined via Euler's phi function and introduced by \textit{R. Yuster} [Discrete Math. 224, 225-237 (2000; Zbl 0982.11007)]. One of the conjectures contained in that paper claims that (*) \(\det (A_n) = (-1)^{n-1}\). This author shows the validity of (*) for \(n\)'s with at most two prime divisors and for even \(n\)'s with at most three prime divisors. Furthermore, (*) holds for \(n\) if it holds for all square-free divisors of \(n.\)