Products of two involutory matrices over skewfields

AbstractIf a simple transformation σ is a product of two involutions, then σ is a reflection or a transvection. This property is still true for matrices over skewfields. It will be used to show that a criterion for the decomposability of a matrix into two involutions, which is known for matrices over commutative fields, is no longer true if the entries of the matrix are taken from a skewfield. Another consequence is that the special linear group of a vector space over the field K is not bireflectional if K is not commutative