diff --git a/src/sage/matrix/matrix2.pyx b/src/sage/matrix/matrix2.pyx
index 2a069660011..34b5808d0c8 100644
--- a/src/sage/matrix/matrix2.pyx
+++ b/src/sage/matrix/matrix2.pyx
@@ -13611,8 +13611,9 @@ cdef class Matrix(Matrix1):
                 if max_location != -1:
                     perm[k], perm[max_location] = perm[max_location], perm[k]
                     M.swap_rows(k, max_location)
+                    inv = M.get_unsafe(k, k).inverse()
                     for j in range(k+1, m):
-                        scale = -M.get_unsafe(j, k)/M.get_unsafe(k, k)
+                        scale = -M.get_unsafe(j, k) * inv
                         M.set_unsafe(j, k, -scale)
                         for p in range(k+1, n):
                             M.set_unsafe(j, p, M.get_unsafe(j, p) + scale*M.get_unsafe(k, p))