Trac #30161: Zero Matrix has Inverse over Finite Field

The bug is outlined in this post:
https://ask.sagemath.org/question/52487/zero-matrix-has-an-inverse-over-
finite-field/

In short, the following lines of code should throw an error, but they do
not.

{{{
M = Matrix([0], ring=GF(4))
M.inverse()
}}}

Instead they return the matrix [1].

URL: https://trac.sagemath.org/30161
Reported by: gh-prismika
Ticket author(s): Martin Albrecht
Reviewer(s): Samuel Lelièvre

src/sage/matrix/matrix_gf2e_dense.pyx

@@ -1019,8 +1019,13 @@ cdef class Matrix_gf2e_dense(matrix_dense.Matrix_dense):
         cdef Matrix_gf2e_dense A
         A = Matrix_gf2e_dense.__new__(Matrix_gf2e_dense, self._parent, 0, 0, 0)
 
-        if self._nrows and self._nrows == self._ncols:
+        if self.rank() != self._nrows:
+            raise ZeroDivisionError("Matrix does not have full rank.")
+
+        if self._nrows:
+            sig_on()
             mzed_invert_newton_john(A._entries, self._entries)
+            sig_off()
 
         return A