Products of involutory matrices. I

It is shown that, for every integer ?1 and every field F, each n×n matrix over F of determinant ±1 is the product of four involutory matrices over F. Products of three ×n involutory matrices over F are characterized for the special cases where n?4 or F has prime order ?5. It is also shown for every field F that every matrix over F of determinant ±1 having no more than two nontrivial invariant factors is a product of three involutory matrices over F.