
theorem
  for V being finite-rank free Z_Module, b1, b2 being OrdBasis of V,
      M being Matrix of rank(V),F_Real st M = AutMt(id(V), b1, b2)
  holds |. Det M .| = 1
  proof
    let V be finite-rank free Z_Module, b1, b2 be OrdBasis of V,
    M be Matrix of rank(V),F_Real;
    assume M = AutMt(id(V), b1, b2);
    then Det M = 1 or Det M = -1 by ThSign2;
    then |. Det M .| = 1 or |. Det M .| = -(-1) by ABSVALUE:def 1;
    hence thesis;
  end;
