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 in INT
  proof
    let V be finite-rank free Z_Module,
    b1, b2 be OrdBasis of V,
    M be Matrix of rank(V),F_Real;
    assume A2: M = AutMt(id(V), b1, b2);
    per cases;
    suppose not 0 < rank(V);
      then rank(V) = 0;
      then Det M = 1.F_Real by MATRIXR2:41;
      hence Det M in INT;
    end;
    suppose A3: 0 < rank(V);
      len M = rank(V) & width M = rank(V) by MATRIX_0:24;
      then M is Matrix of rank(V),INT by A2,A3,MATRIX_0:20;
      hence thesis by LmSign1A;
    end;
  end;
