[DB/MySQL] Help mapping a relationship

[Augmented]

Brain's not working at full capacity today. I'm trying to figure out the best way to create a relationship between a set of objects and the owners of each object. Note this is the principle of what I'm doing, 'objects' are an abstract term here .

I have a table where each row contains a unique object, and a table of unique 'owners' of objects. One or many of the owners may own an object:

OBJECTS
id	int(11)	PK
object	varchar(255)

OWNERS
id	int(11)	PK
owner	varchar(255)

It's been a couple of years since I did any DB theory, but this is a many-to-many relationship, right?

I wish to be able to query for an object and see who owns it and vice-versa.
I have a mapping table:

ID	object_id	owner_id
1	 1		 1
2	 1		 2
3	 1		 3
4	 2		 1
5	 2		 3
6	 3		 3

Is this the best way to do it? Can anyone see any pitfalls with this?
Would it be better to remove the ID column, and instead create a PK of object_id and owner_id?

 

[Augmented]

Thanks for the replies; always helpful to get the second opinion .
Will be using the compound key - makes sense. Adding an auto_increment ID field for the primary key starts becoming a habit with MySQL - you just add it without really thinking whether there's a better option.