Run “USE” with linked server alternatives

Question

I am using SQL server linked servers and find some difficulties while running queries.

Below is the actual query.

USe testdb
SELECT COLUMNPROPERTY( OBJECT_ID('Table_1'),'column1','IsIdentity')

It returns 1 as column1 is identity column 
To run it to a linked server I used

Use mylinkedserver.testdb
SELECT COLUMNPROPERTY(OBJECT_ID('Table_1'),'column1','IsIdentity') 

But when I run this I get error as shown below Database 'mylinkedserver' does not exist. Make sure that the name is entered correctly.

Where as I can query the table by using select * from pc91sql.testdb.dbo.Table_1 successfully.

Then i used OPENQUERY option

SELECT * FROM OPENQUERY(pc91sql,'SELECT COLUMNPROPERTY( OBJECT_ID(''testdb.dbo.Table_1''),''column1'',''IsIdentity'')');

It returned NULL. But it should have returned 1 as column1 is a identity column.

Then I checked again running my original query directly in the linked server without use command and NULL is returned . If I run same query after I mention use testdb or in SSMS after choosing database from list then it returns 1 .So it means OBJECT_ID is not able to use database name along with table name(i.e like ''testdb.dbo.Table_1'').


So how to run the above query?(I think i cannot make use of "USE" with linked server.So what is the alternative