<Grid>
  <Grid.RowDefinitions>
    <RowDefinition/>
    <RowDefinition Height="Auto"/>
    <RowDefinition Height="Auto"/>
    <RowDefinition Height="Auto"/>
  </Grid.RowDefinitions>
  <DataGrid
    x:Name="dataGrid"
    ItemsSource="{Binding Items}"
    SelectionMode="Single"
    SelectedItem="{Binding SelectedItem, Mode=TwoWay, UpdateSourceTrigger=PropertyChanged}"
    IsSynchronizedWithCurrentItem="True"
    IsReadOnly="True"
    AutoGenerateColumns="False">
    <DataGrid.Columns>
      <DataGridTextColumn
        Binding="{Binding Path=A}"
        Header="A"
        Width="*"/>
      <DataGridTextColumn
        Binding="{Binding Path=B}"
        Header="B"
        Width="*"/>
    </DataGrid.Columns>
  </DataGrid>
  <Button
    Grid.Row="1"
    Content="Delete selected"
    Padding="5"
    Margin="5"
    HorizontalAlignment="Center"
    VerticalAlignment="Center"
    Command="{Binding DeleteCommand}"/>
  <Button
    Grid.Row="2"
    Content="Check binding"
    Padding="5"
    Margin="5"
    HorizontalAlignment="Center"
    VerticalAlignment="Center"
    Click="CheckBinding"/>
  <Button
    Grid.Row="3"
    Content="Go to last"
    Padding="5"
    Margin="5"
    HorizontalAlignment="Center"
    VerticalAlignment="Center"
    Command="{Binding GoLastCommand}"/>
</Grid>

public partial class MainWindow : INotifyPropertyChanged
{
  [DllImport("kernel32.dll",
    EntryPoint = "AllocConsole",
    SetLastError = true,
    CharSet = CharSet.Auto,
    CallingConvention = CallingConvention.StdCall)]
  static extern int AllocConsole();

  public MainWindow()
  {
    InitializeComponent();
    AllocConsole();
    Items = new ObservableCollection<Foo>(Enumerable.Range(1, 10).Select(i => new Foo {A = i, B = i}).ToList());
    DeleteCommand = new RelayCommand(DeleteSelectedItem, () => SelectedItem != null);
    GoLastCommand = new RelayCommand(() => SelectedItem = Items.Last());
    SelectedItem = Items.First();
    DataContext = this;
  }

  public ObservableCollection<Foo> Items { get; private set; }
  public RelayCommand DeleteCommand { get; private set; }
  public RelayCommand GoLastCommand { get; private set; }

  void DeleteSelectedItem()
  {
    SelectedItem.B++;
    Items.Remove(SelectedItem);
  }

  Foo _selectedItem;
  public Foo SelectedItem
  {
    get { return _selectedItem; }
    set
    {
      Console.WriteLine("SelectedItem: {0}", value);
      _selectedItem = value;
      RaisePropertyChanged("SelectedItem");
      DeleteCommand.RaiseCanExecuteChanged();
    }
  }

  public event PropertyChangedEventHandler PropertyChanged;
  void RaisePropertyChanged(string propertyName)
  {
    var pc = PropertyChanged;
    if(pc!=null)
      pc(this, new PropertyChangedEventArgs(propertyName));
  }

  void CheckBinding(object sender, System.Windows.RoutedEventArgs e)
  {
    var b = dataGrid.GetBindingExpression(Selector.SelectedItemProperty);
    if (b==null)
    {
      Console.WriteLine("null");
      return;
    }
    Console.WriteLine("{0} {1} {2} {3}",b.Status, b.HasError, b.ParentBinding.Path.Path, b.ParentBinding.Mode);
  }
}

public class Foo
{
  public int A { get; set; }
  public int B { get; set; }
  public override int GetHashCode()
  {
    return A*10+B;
  }
  public override bool Equals(object obj)
  {
    var f = obj as Foo;
    return f!=null && f.A==A && f.B==B;
  }
  public override string ToString()
  {
    return string.Format("Foo {{ A={0}, B={1} }}", A, B);
  }
}