Making some additional improvements.

src/sage/groups/matrix_gps/coxeter_group.py

@@ -509,9 +509,10 @@ def has_right_descent(self, i):
             i = self.parent().index_set().index(i)
             n = len(self.parent().index_set())
             M = self.matrix()
+            zero = M.base_ring().zero()
             # When working over the UCF, this is the bottleneck because it has
             #   to convert the entries to QQbar and do the comparison there.
-            return all(M[j,i] <= 0 for j in range(n))
+            return all(M[j,i] <= zero for j in range(n))
 
         def canonical_matrix(self):
             r"""

src/sage/groups/matrix_gps/group_element.py

@@ -322,8 +322,10 @@ def _mul_(self,other):
             [0 1]
         """
         parent = self.parent()
-        return parent.element_class(parent, self._matrix * other._matrix,
-                                    check=False, convert=False)
+        M = self._matrix * other._matrix
+        # Make it immutable so the constructor doesn't make a copy
+        M.set_immutable()
+        return parent.element_class(parent, M, check=False, convert=False)
 
     def __invert__(self):
         """
@@ -347,7 +349,10 @@ def __invert__(self):
            [0 1]
         """
         parent = self.parent()
-        return parent.element_class(parent, ~self._matrix, check=False, convert=False)
+        M = ~self._matrix
+        # Make it immutable so the constructor doesn't make a copy
+        M.set_immutable()
+        return parent.element_class(parent, M, check=False, convert=False)
 
     inverse = __invert__