
theorem Th13:
  for N1,N2 being Matrix of 3,F_Real st
  N1 = <* <* 2,   0,   -1 *>,
          <* 0, sqrt 3, 0 *>,
          <* 1,   0,   -2 *> *> &
  N2 = <* <* 2/3,     0,     -1/3 *>,
          <* 0,    1/sqrt 3,    0 *>,
          <* 1/3,     0,     -2/3 *> *>
  holds N1 is_reverse_of N2
  proof
    let N1,N2 be Matrix of 3,F_Real;
    assume
A1: N1 = <* <* 2,   0,    -1 *>,
            <* 0, sqrt 3,  0 *>,
            <* 1,   0,    -2 *> *> &
    N2 = <* <* 2/3,   0,      -1/3 *>,
            <* 0,   1/sqrt 3,    0 *>,
            <* 1/3,   0,      -2/3 *> *>;
    N2 * N1 = 1.(F_Real,3) & N1 * N2 = 1.(F_Real,3) by A1,Th11,Th12,ANPROJ_9:1;
    hence thesis by MATRIX_6:def 2;
  end;
