diff --git a/src/sage/matrix/matrix_integer_dense.pyx b/src/sage/matrix/matrix_integer_dense.pyx
index d582393e565..a1ad92fa58b 100644
--- a/src/sage/matrix/matrix_integer_dense.pyx
+++ b/src/sage/matrix/matrix_integer_dense.pyx
@@ -1416,7 +1416,7 @@ cdef class Matrix_integer_dense(Matrix_dense):
                 sig_on()
                 linbox_fmpz_mat_charpoly(g._poly, self._matrix)
                 sig_off()
-                if g.lc() == 1:
+                if g.lc() == 1 and g.degree() == self._nrows:
                     break
         elif algorithm == 'generic':
             g = Matrix_dense.charpoly(self, var)
diff --git a/src/sage/matrix/matrix_integer_sparse.pyx b/src/sage/matrix/matrix_integer_sparse.pyx
index 9c68b951907..dc961d53f44 100644
--- a/src/sage/matrix/matrix_integer_sparse.pyx
+++ b/src/sage/matrix/matrix_integer_sparse.pyx
@@ -912,7 +912,7 @@ cdef class Matrix_integer_sparse(Matrix_sparse):
                 fmpz_poly_set_coeff_mpz(g._poly, i, tmp)
             _fmpz_poly_set_length(g._poly, p.size())
 
-            if g.lc() == 1:
+            if g.lc() == 1 and g.degree() == self._nrows:
                 break
 
         del M