public void SelectLayers( 
   IReadOnlyCollection<Layer> layers
)

public void SelectAllFeatureLayersInTOC()
{
  //Get the active map view.
  var mapView = MapView.Active;
  if (mapView == null)
    return;

  //Zoom to the selected layers in the TOC
  var featureLayers = mapView.Map.Layers.OfType<FeatureLayer>();
  mapView.SelectLayers(featureLayers.ToList());
}

// get the layer you want
var layer = MapView.Active.Map.GetLayersAsFlattenedList().OfType<FeatureLayer>().FirstOrDefault();

// select it in the TOC
List<Layer> layersToSelect = new List<Layer>();
layersToSelect.Add(layer);
MapView.Active.SelectLayers(layersToSelect);

// now execute the layer properties command
var wrapper = FrameworkApplication.GetPlugInWrapper("esri_mapping_selectedLayerPropertiesButton");
var command = wrapper as ICommand;
if (command == null)
  return;

// execute the command
if (command.CanExecute(null))
  command.Execute(null);