
theorem
  for m be non zero Element of NAT,
      f be Point of
        R_NormSpace_of_BoundedLinearOperators(REAL-NS m, REAL-NS m),
      M be Matrix of m, F_Real
    st f = Mx2Tran(M)
  holds
    f is invertible
      iff
    Det M <> 0.F_Real
proof
  let m be non zero Element of NAT,
      f be Point of
        R_NormSpace_of_BoundedLinearOperators (REAL-NS m, REAL-NS m),
      M be Matrix of m, F_Real;
  assume f = Mx2Tran(M);
  then
  f is invertible
    iff
  M is invertible by Th12;

  hence thesis by LAPLACE:34;
end;
