Trace identities from identities for determinants

We present new identities for determinants of matrices (Ai,j) with entries (Ai,j) equal to (ai,j) or ai,0a0,j − ai,j, where the ai,j's are indeterminates. We show that these identities are behind trace identities for SL(2,C) matrices found earlier by Magnus in his study of trace algebras.