gretl 2020e Windows 64

I created a "residual maker" matrix M = I - X*inv(X'X)*X', which is symmetric, non-invertible and  idempotent. Below I have copied  its properties as printed out by gretl. It clearly states that the matrix is "Not idempotent".

But It is, in theory and it is in practice: I performed the operation M*M - M, and I got a matrix with zeros or numbers raised to the 10^{-16} or even smaller.

What does it take for gretl to characterize a matrix as idempotent?

**************************************

Properties of matrix M

Rows          50
Columns       50
Rank          47
Square
Not idempotent

1-norm           3.0108809
Infinity-norm    3.0108809
Trace            47
Determinant      4.0749073e-047

Eigenvalues:
  (1.586419e-015, 0)
  (-1.300316e-015, 0)
  (3.561026e-017, 0)
  (1, 0)
  (1, 0)
  (1, 0)
  (1, 0)
  (1, 0)
  (1, 0)
  (1, 0)
  (1, 0)
  (1, 0)
  (1, 0)
  (1, 0)
  (1, 0)
  (1, 0)
  (1, 0)
  (1, 0)
  (1, 0)
  (1, 0)
  (1, 0)
  (1, 0)
  (1, 0)
  (1, 0)
  (1, 0)
  (1, 0)
  (1, 0)
  (1, 0)
  (1, 0)
  (1, 0)
  (1, 0)
  (1, 0)
  (1, 0)
  (1, 0)
  (1, 0)
  (1, 0)
  (1, 0)
  (1, 0)
  (1, 0)
  (1, 0)
  (1, 0)
  (1, 0)
  (1, 0)
  (1, 0)
  (1, 0)
  (1, 0)
  (1, 0)
  (1, 5.5511151e-017)
  (1, -5.5511151e-017)
  (1, 0)

-- 
Alecos Papadopoulos PhD
Athens University of Economics and Business
web: alecospapadopoulos.wordpress.com/
scholar:https://g.co/kgs/BqH2YU