Good easy question, but I do not agree with the answers explination.

A unique constraint is what a table needs to garuntee an column does not repeat values.

Making a column part of a Primary Key value does create a constraint for Unique values.

That is the effect not the cause.

If both columns in the table are selected as Primary Key, then you could still insert duplicates into the Unique_Id column.

Make sure your Identity columns have there own Unique Index and/or value constraint and you don't have to worry about dupes.