TITLE: Faithful Representations of C*-algebras
QUESTION [5 upvotes]: Can anyone give me an example of a represetation of the algebra $M_n(\mathbb{C})$ that is not faithul?
If it's not possible, could you explain me why it is not?

REPLY [15 votes]: Apart from the zero representation, every representation of $M_n$ is faithful. It follows from the fact that $M_n$ is simple, meaning it has no non-trivial ideals.