Indexes and multi column primary keys

In a MySQL database I have a table with the following primary key

PRIMARY KEY id (invoice, item)

In my application I will also frequently be selecting on item by itself and less frequently on only invoice. I'm assuming I would benefit from indexes on these columns.

MySQL does not complain when I define the following:

INDEX (invoice),
INDEX (item),
PRIMARY KEY id (invoice, item)

But I don't see any evidence (using DESCRIBE -- the only way I know how to look) that separate indexes have been established for these two columns.

Are the columns that make up a primary key automatically indexed individually? Is there a better way than DESCRIBE to explore the structure of my table?