reserve a,b,c,d,e,f for Real,
        g           for positive Real,
        x,y         for Complex,
        S,T         for Element of REAL 2,
        u,v,w       for Element of TOP-REAL 3;
reserve a,b,c for Element of F_Real,
          M,N for Matrix of 3,F_Real;
reserve D        for non empty set;
reserve d1,d2,d3 for Element of D;
reserve A        for Matrix of 1,3,D;
reserve B        for Matrix of 3,1,D;
reserve u,v for non zero Element of TOP-REAL 3;

theorem Th44:
  symmetric_3(1,1,-1,0,0,0) is invertible Matrix of 3,F_Real &
  (symmetric_3(1,1,-1,0,0,0))~ = symmetric_3(1,1,-1,0,0,0)
  proof
A1: symmetric_3(1,1,-1,0,0,0) is_reverse_of symmetric_3(1,1,-1,0,0,0)
      by Th43,MATRIX_6:def 2;
    thus symmetric_3(1,1,-1,0,0,0) is invertible Matrix of 3,F_Real
      by Th43,MATRIX_6:def 2,MATRIX_6:def 3;
    hence (symmetric_3(1,1,-1,0,0,0))~ = symmetric_3(1,1,-1,0,0,0)
      by A1,MATRIX_6:def 4;
  end;
