diff --git a/reference/test/matrix/batch_csr_kernels.cpp b/reference/test/matrix/batch_csr_kernels.cpp
index 0464e922976..d1df7e4296f 100644
--- a/reference/test/matrix/batch_csr_kernels.cpp
+++ b/reference/test/matrix/batch_csr_kernels.cpp
@@ -222,6 +222,22 @@ TYPED_TEST(Csr, CanAddScaledIdentity)
 }
 
 
+TYPED_TEST(Csr, AddScaledIdentityFailsOnMatrixWithoutDiagonal)
+{
+    using BMtx = typename TestFixture::BMtx;
+    using BMVec = typename TestFixture::BMVec;
+    auto alpha = gko::batch::initialize<BMVec>({{2.0}, {-1.0}}, this->exec);
+    auto beta = gko::batch::initialize<BMVec>({{3.0}, {-2.0}}, this->exec);
+    auto mat = gko::batch::initialize<BMtx>(
+        {{{0.0, 2.0, 0.0}, {3.0, 1.0, 1.0}, {0.0, 1.0, 1.0}},
+         {{0.0, -2.0, 0.0}, {1.0, -1.0, 2.0}, {0.0, 2.0, 1.0}}},
+        this->exec, 6);
+
+    ASSERT_THROW(mat->add_scaled_identity(alpha, beta),
+                 gko::UnsupportedMatrixProperty);
+}
+
+
 TYPED_TEST(Csr, ApplyFailsOnWrongNumberOfResultCols)
 {
     using BMVec = typename TestFixture::BMVec;
diff --git a/reference/test/matrix/batch_ell_kernels.cpp b/reference/test/matrix/batch_ell_kernels.cpp
index b0b41941038..f4d8b131247 100644
--- a/reference/test/matrix/batch_ell_kernels.cpp
+++ b/reference/test/matrix/batch_ell_kernels.cpp
@@ -224,6 +224,22 @@ TYPED_TEST(Ell, CanAddScaledIdentity)
 }
 
 
+TYPED_TEST(Ell, AddScaledIdentityFailsOnMatrixWithoutDiagonal)
+{
+    using BMtx = typename TestFixture::BMtx;
+    using BMVec = typename TestFixture::BMVec;
+    auto alpha = gko::batch::initialize<BMVec>({{2.0}, {-1.0}}, this->exec);
+    auto beta = gko::batch::initialize<BMVec>({{3.0}, {-2.0}}, this->exec);
+    auto mat = gko::batch::initialize<BMtx>(
+        {{{0.0, 2.0, 1.0}, {0.0, 1.0, 1.0}, {0.0, 1.0, 1.0}},
+         {{0.0, -2.0, 2.0}, {0.0, -1.0, 2.0}, {0.0, 2.0, 1.0}}},
+        this->exec, 2);
+
+    ASSERT_THROW(mat->add_scaled_identity(alpha, beta),
+                 gko::UnsupportedMatrixProperty);
+}
+
+
 TYPED_TEST(Ell, ApplyFailsOnWrongNumberOfResultCols)
 {
     using BMVec = typename TestFixture::BMVec;