How can I root the GT 10.1 (running 3.2)?
With 3.2 Google fixed the exploit that allowed most current methods to gain root on 3.1 version.  The only way to get root on Galaxy Tab 10.1 running Android 3.2 is to flash a pre-rooted ROM via Odin (or Heimdal) utility.  Take a look at the appropriate section on XDA-Developers forum for more details.

This completely wipes all data off the device, so it's recommended to back up anything you need first.  Also, be sure to pick the correct ROM for your specific version of the Tab, since 
different versions (WiFi-only Vs. 3G) will require separate ROMs.