sagemath · HenryWu2101 · Mar 27, 2025 · Apr 4, 2025 · Apr 4, 2025 · Apr 5, 2025
diff --git a/src/sage/matrix/matrix_gf2e_dense.pyx b/src/sage/matrix/matrix_gf2e_dense.pyx
@@ -963,6 +963,22 @@
                 break
         return pivots
 
+    def is_invertible(self):
+        """
+        Return ``True`` if this matrix is invertible.
+
-
+
+        ALGORITHM: this checks that the matrix is square and has full rank. This is to circumvent the determinant computation used by the general method :meth:`sage.matrix.matrix0.Matrix.is_invertible`, since currently there is no efficient determinant implementation in this class of matrices.
-
+
+        ALGORITHM: this checks that the matrix is square and has full rank. This is to circumvent the determinant computation used by the general method :meth:`sage.matrix.matrix0.Matrix.is_invertible`, since currently there is no efficient determinant implementation in this class of matrices.
+        EXAMPLES::
+
+            sage: m = Matrix(GL(2^8, GF(2^8)).random_element())
+            sage: m.is_invertible()
+            True
+        """
+        if self._ncols != self._nrows:
+            return False
+        if self._nrows != self.rank():
+            return False
+        return True
+
     def __invert__(self):
         """
         EXAMPLES::
@@ -980,7 +996,7 @@
         cdef Matrix_gf2e_dense A
         A = Matrix_gf2e_dense.__new__(Matrix_gf2e_dense, self._parent, 0, 0, 0)
 
-        if self.rank() != self._nrows:
+        if not self.is_invertible():
             raise ZeroDivisionError("Matrix does not have full rank.")
 
         if self._nrows: