reserve i,j,n,k for Nat,
  a for Element of COMPLEX,
  R1,R2 for Element of i-tuples_on COMPLEX;

theorem
  for M being Matrix of COMPLEX holds (-M)*' = -(M*')
proof
  let M be Matrix of COMPLEX;
  (-M)*'= ((-1)*M)*' by Th10
    .= ((-1r)*')*(M*') by Th4,COMPLEX1:def 4
    .= (-1)*(M*') by COMPLEX1:30,33,def 4
    .= -M*' by Th10;
  hence thesis;
end;
