Invariant polynomial

Hello,

I was reading over the usage of trace of a matrix and came across that trace is the simplest non-trivial example of an invariant polynomial.

I have few questions:

(a) What is an example of an invariant polynomial?

(b) I learned that the the values of an invariant polynomial is co-ordinate independent. Can you please give me an example?

(c) The det.of a matrix is also an invariant polynomial. How it is so? An example please.

Thanks,

-- Shounak