diff --git a/core/test/matrix/permutation.cpp b/core/test/matrix/permutation.cpp
index 6545dcc5d6b..1681b2f9e51 100644
--- a/core/test/matrix/permutation.cpp
+++ b/core/test/matrix/permutation.cpp
@@ -100,6 +100,15 @@ TEST_F(Permutation, ReturnsNullValuesArrayWhenEmpty)
 }
 
 
+TEST_F(Permutation, FactorySetsCorrectPermuteMask)
+{
+    auto m = gko::matrix::Permutation<i_type>::create(exec);
+    auto mask = m->get_permute_mask();
+
+    ASSERT_EQ(mask, gko::matrix::row_permute);
+}
+
+
 TEST_F(Permutation, CanBeConstructedWithSize)
 {
     auto m = gko::matrix::Permutation<i_type>::create(exec, gko::dim<2>{2, 3});
@@ -109,6 +118,33 @@ TEST_F(Permutation, CanBeConstructedWithSize)
 }
 
 
+TEST_F(Permutation, CanBeConstructedWithSizeAndMask)
+{
+    auto m = gko::matrix::Permutation<i_type>::create(
+        exec, gko::dim<2>{2, 3}, gko::matrix::column_permute);
+
+    ASSERT_EQ(m->get_size(), gko::dim<2>(2, 3));
+    ASSERT_EQ(m->get_permutation_size(), 2);
+    ASSERT_EQ(m->get_permute_mask(), gko::matrix::column_permute);
+}
+
+
+TEST_F(Permutation, CanExplicitlyOverrideSetPermuteMask)
+{
+    auto m = gko::matrix::Permutation<i_type>::create(
+        exec, gko::dim<2>{2, 3}, gko::matrix::column_permute);
+
+    auto mask = m->get_permute_mask();
+    ASSERT_EQ(mask, gko::matrix::column_permute);
+
+    m->set_permute_mask(gko::matrix::row_permute |
+                        gko::matrix::inverse_permute);
+
+    auto s_mask = m->get_permute_mask();
+    ASSERT_EQ(s_mask, gko::matrix::row_permute | gko::matrix::inverse_permute);
+}
+
+
 TEST_F(Permutation, PermutationCanBeConstructedFromExistingData)
 {
     i_type data[] = {1, 0, 2};
@@ -120,6 +156,26 @@ TEST_F(Permutation, PermutationCanBeConstructedFromExistingData)
 }
 
 
+TEST_F(Permutation, SettingMaskDoesNotModifyData)
+{
+    i_type data[] = {1, 0, 2};
+
+    auto m = gko::matrix::Permutation<i_type>::create(
+        exec, gko::dim<2>{3, 5}, gko::Array<i_type>::view(exec, 3, data));
+
+    auto mask = m->get_permute_mask();
+    ASSERT_EQ(m->get_const_permutation(), data);
+    ASSERT_EQ(mask, gko::matrix::row_permute);
+
+    m->set_permute_mask(gko::matrix::row_permute |
+                        gko::matrix::inverse_permute);
+
+    auto s_mask = m->get_permute_mask();
+    ASSERT_EQ(s_mask, gko::matrix::row_permute | gko::matrix::inverse_permute);
+    ASSERT_EQ(m->get_const_permutation(), data);
+}
+
+
 TEST_F(Permutation, PermutationThrowsforWrongRowPermDimensions)
 {
     i_type data[] = {0, 2, 1};
@@ -163,6 +219,31 @@ TEST_F(Permutation, CanBeCopied)
 }
 
 
+TEST_F(Permutation, CopyingPreservesMask)
+{
+    auto mtx_copy = gko::matrix::Permutation<i_type>::create(exec);
+
+    mtx_copy->copy_from(mtx.get());
+
+    auto o_mask = mtx->get_permute_mask();
+    auto n_mask = mtx_copy->get_permute_mask();
+    ASSERT_EQ(o_mask, gko::matrix::row_permute);
+    ASSERT_EQ(o_mask, n_mask);
+
+    mtx->set_permute_mask(gko::matrix::column_permute);
+
+    o_mask = mtx->get_permute_mask();
+    n_mask = mtx_copy->get_permute_mask();
+    ASSERT_EQ(o_mask, gko::matrix::column_permute);
+    ASSERT_NE(o_mask, n_mask);
+
+    mtx_copy->copy_from(mtx.get());
+
+    n_mask = mtx_copy->get_permute_mask();
+    ASSERT_EQ(o_mask, n_mask);
+}
+
+
 TEST_F(Permutation, CanBeMoved)
 {
     auto mtx_copy = gko::matrix::Permutation<i_type>::create(exec);
diff --git a/include/ginkgo/core/matrix/permutation.hpp b/include/ginkgo/core/matrix/permutation.hpp
index f8c01ab24e6..a273d250017 100644
--- a/include/ginkgo/core/matrix/permutation.hpp
+++ b/include/ginkgo/core/matrix/permutation.hpp
@@ -114,6 +114,23 @@ class Permutation : public EnableLinOp<Permutation<IndexType>>,
         return permutation_.get_num_elems();
     }
 
+    /**
+     * Get the permute masks
+     *
+     * @param permute_mask the permute masks
+     */
+    mask_type get_permute_mask() { return enabled_permute_; }
+
+    /**
+     * Set the permute masks
+     *
+     * @param permute_mask the permute masks
+     */
+    void set_permute_mask(mask_type permute_mask)
+    {
+        enabled_permute_ = permute_mask;
+    }
+
 
 protected:
     /**
@@ -122,7 +139,7 @@ class Permutation : public EnableLinOp<Permutation<IndexType>>,
      * @param exec  Executor associated to the LinOp
      */
     Permutation(std::shared_ptr<const Executor> exec)
-        : Permutation(std::move(exec), dim<2>{})
+        : Permutation(std::move(exec), dim<2>{}, row_permute)
     {}
 
     /**