The Collatz function \(f\) on \(\mathbb{N}\) is defined by \(f(n)=n/2\) for even \(n\), and \(f(n)=(3n+1)/2\) for odd \(n\). Let \(A=(a_{ij})\) be the infinite matrix with \(a_{ij}=\delta_{f(i),j}\), where \(\delta\) is the Kronecker delta, and let \(A_n\) be its leading \(n\times n\) principal submatrix. For \(n\ge 3\), let \(C_n\) be the \((n-2)\times (n-2)\) principal submatrix of \(A_n\) with entries \(a_{ij}\) for \(3\le i,j\le n\). The author proves that the conjecture stating the nilpotence of any \(C_n\) is equivalent to the Collatz conjecture. This extends the work of J. F. Alves et al. [Linear Algebra Appl. 394, 277–289 (2005; Zbl 1116.11012)] and simplifies a conjecture by D. A. Cardon and B. Tuckfield [Linear Algebra Appl. 435, 2942–2954 (2011; Zbl 1229.15013)].