Integer matrix factorisations, superalgebras and the quadratic form obstruction

We identify and analyse obstructions to factorisation of integer matrices into products NTN or N2 with rational entries. The arise as quadratic forms coefficients raise the question discrete range such forms. They are obtained by considering matrix decompositions over a superalgebra. further obtain formula for determinant square in terms adjugates these decompositions, well identifying co-Latin symmetry space.