To get Task Manager into the System Tray:

1. Open Task Manager.

2. On the Options menu, check Hide When Minimized.

3. Minimize Task Manager.

If you always want it there:

1. Navigate to %SystemRoot%\System32\Taskmgr.exe.

2. Right click and create a shortcut.

3. Move it to your Startup folder.

4. Right click the shortcut and choose Properties.

5. Set it to start Minimized.