2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115186We present several non-commutative extensions of the MacMahon Master Theorem, further extending the results of Cartier-Foata and Garoufalidis-Le-Zeilberger. The proofs are combinatorial and new even in the classical cases. We also give applications to the $β$-extension and Krattenthaler-Schlosser's $q$-analogue.28 pages, 6 figuresCombinatorics05A05; 05A30; 05E15text