Problem inverting complex matrix

[jesuscf]

Consider this complex matrix:

M1 =
\begin{bmatrix}
0.0005 & 0 & 0 & -0.0005 & 0 & 0 & 0 & 1 \\
0 & 9.69696969697E-4+0.00125i & 0 & -0.00125i & -6.66666666667E-4 & -3.0303030303E-4 & 0 & 0 \\
0 & 0 & 3.57142857143E-4-0.0025i & 0 & 0.0025i & 0 & -3.57142857143E-4 & 0 \\
-0.0005 & -0.00125i & 0 & 0.0005+0.00125i & 0 & 0 & 0 & 0 \\
0 & -6.66666666667E-4 & 0.0025i & 0 & 6.66666666667E-4-0.0025i & 0 & 0 & 0 \\
0 & -3.0303030303E-4 & 0 & 0 & 0 & 3.0303030303E-4-1.66666666667E-3i & 0 & 0 \\
0 & 0 & -3.57142857143E-4 & 0 & 0 & 0 & 3.57142857143E-4+0.005i & 0 \\
1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
\end{bmatrix}

Inverting with the HP-Prime using 1/M1 works:
   

Inverting it using inv(M1) fails.
   

Is this a bug or there is something I failed to consider?

If you want to try, M1.hpmat is included in this zip file:

  M1.zip (Size: 289 bytes / Downloads: 9)