[dba-SQLServer] Which machine does the work?

I have two machines, both running SQL Server instances.  MachineA has
registered the database on MachineA and the database on MachineB.  MachineB
has done likewise.   MachineA holds a database with a table to which I want
to add an index.  If I open EM on MachineB, select the database on MachineA,
open a table in design view and "add an index", where is the work performed?
Does MachineB actually do anything?  Or does MachineB simply send a command
to the SQL Server instance on MachineA telling it to add the index and all
of the work is performed on MachineA?
 
John W. Colby
Colby Consulting
www.ColbyConsulting.com