On a unification result by A. R. Sourour concerning commutators and products of involutions (Q2496657)

Let \(F\) be a field with at least four elements and let \(A\) be a square matrix with entries in \(F\). The author shows that \(A\) is a product of two diagonalizable matrices, that \(A\) is a commutator if and only if \(\det A=1\) and \(A\) is a product of four or fewer involutions if \(\det A=\pm 1\). Similar results were obtained by \textit{A. R. Sourour} [Linear Multilinear Algebra 19, 141--147 (1986; Zbl 0591.15008)], but Sourour requires occasionally fields with more elements than are required in the present paper.