theorem LmSign3:
  for V being finite-rank free Z_Module, b1, b2 being OrdBasis of V
  st rank(V) > 0
  holds (AutMt(id(V), b1, b2)) * (AutMt(id(V), b2, b1)) = 1.(INT.Ring,rank(V))
  proof
    let V be finite-rank free Z_Module, b1, b2 be OrdBasis of V;
    assume AS: rank(V) > 0;
    then A1: len b1 > 0 & len b2 > 0 by ThRank1;
    thus (AutMt(id(V), b1, b2))
    * (AutMt(id(V), b2, b1)) =
    AutMt(id(V)*id(V), b1, b1) by A1,ThComp1
    .= AutMt(id(V), b1, b1) by FUNCT_2:17
    .= 1.(INT.Ring,rank(V)) by AS,LmSign31;
  end;
