Can access control matrix in addition to confidentiality provide the integrity of the objects to which access is being controlled?
Of course! Yes, absolutely. To explain I need to give a refresher on these terms.
What's an access control matrix? It's a matrix A, where Ai,j indicates the permissions that subject i has to access resource j. The permissions might be something like "read" or "read,write" or "read,execute". The access control matrix is an abstraction that captures the policy that is enforced by an access control mechanism.
So, can you use access control to protect the integrity of a resource? Sure. Just limit who receives write permission to that resource to only entities who are trusted not to screw up its integrity. This is indeed one of the primary motivations for access control.
In theory, yes. The Biba integrity matrix is the traditional theoretical description of such an ACL. Unfortunately it turns out to be rather difficult to describe "integrity" in a way that facilitate development of a Biba based system. I'm not aware of any real world implementations of Biba, although if I remember correctly, the concept was applied to parts of the Trusted Computing Station.