On a unification result by A.R. Sourour concerning commutators and products of involutions

Sourour [A.R. Sourour, A factorization theorem for matrices, Linear and Multilinear Algebra 19 (1986) 141–147] presented a factorization theorem for nonsingular matrices, and demonstrated how it could be used to unify some matrix factorization results concerning commutators and products of involutions over an arbitrary field with sufficiently many elements (in particular, an infinite field). The purpose of this paper is to present similar results which are valid over an arbitrary field with at least four elements.