diff --git a/src/backends/meta-input-settings.c b/src/backends/meta-input-settings.c
index 045df81de..0fcac9095 100644
--- a/src/backends/meta-input-settings.c
+++ b/src/backends/meta-input-settings.c
@@ -1082,24 +1082,19 @@ update_device_display (MetaInputSettings  *input_settings,
   priv = meta_input_settings_get_instance_private (input_settings);
   input_settings_class = META_INPUT_SETTINGS_GET_CLASS (input_settings);
 
-  /* If mapping is relative, the device can move on all displays */
-  if (clutter_input_device_get_device_type (device) == CLUTTER_TOUCHSCREEN_DEVICE ||
-      clutter_input_device_get_mapping_mode (device) ==
-      CLUTTER_INPUT_DEVICE_MAPPING_ABSOLUTE)
+  meta_input_settings_find_monitor (input_settings, settings, device,
+                                    &monitor, &logical_monitor);
+  if (monitor)
     {
-      meta_input_settings_find_monitor (input_settings, settings, device,
-                                        &monitor, &logical_monitor);
-      if (monitor)
-        {
-          meta_input_mapper_remove_device (priv->input_mapper, device);
-          meta_monitor_manager_get_monitor_matrix (priv->monitor_manager,
-                                                   monitor, logical_monitor, matrix);
-        }
-      else
-        {
-          if (meta_input_settings_delegate_on_mapper (input_settings, device))
-            return;
-        }
+      meta_input_mapper_remove_device (priv->input_mapper, device);
+      meta_monitor_manager_get_monitor_matrix (priv->monitor_manager,
+                                               monitor, logical_monitor,
+                                               matrix);
+    }
+  else
+    {
+      if (meta_input_settings_delegate_on_mapper (input_settings, device))
+        return;
     }
 
   input_settings_class->set_matrix (input_settings, device, matrix);
diff --git a/src/backends/native/meta-input-settings-native.c b/src/backends/native/meta-input-settings-native.c
index 6f4ff6ba7..9ad28452d 100644
--- a/src/backends/native/meta-input-settings-native.c
+++ b/src/backends/native/meta-input-settings-native.c
@@ -70,8 +70,19 @@ meta_input_settings_native_set_matrix (MetaInputSettings  *settings,
 {
   cairo_matrix_t dev_matrix;
 
-  cairo_matrix_init (&dev_matrix, matrix[0], matrix[3], matrix[1],
-                     matrix[4], matrix[2], matrix[5]);
+  if (clutter_input_device_get_device_type (device) ==
+      CLUTTER_TOUCHSCREEN_DEVICE ||
+      clutter_input_device_get_mapping_mode (device) ==
+      CLUTTER_INPUT_DEVICE_MAPPING_ABSOLUTE)
+    {
+      cairo_matrix_init (&dev_matrix, matrix[0], matrix[3], matrix[1],
+                         matrix[4], matrix[2], matrix[5]);
+    }
+  else
+    {
+      cairo_matrix_init_identity (&dev_matrix);
+    }
+
   g_object_set (device, "device-matrix", &dev_matrix, NULL);
 }