2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/95870We present new identities for determinants of matrices $(A_{i,j})$ with entries $A_{i,j}$ equal to $a_{i,j}$ or $a_{i,0}a_{0,j}-a_{i,j}$, where the $a_{i,j}$'s are indeterminates. We show that these identities are behind trace identities for $SL(2,\Bbb C)$ matrices found earlier by Magnus in his study of trace algebras.14 pages, AmS-TeXCommutative AlgebraCombinatoricsRings and AlgebrasPrimary 15A15; Secondary 13B25 20G20text