Let A be 2x2 and let $\displaystyle p(\lambda)=\lambda^2+b\lambda+c$ be the characteristic polynomial of A. Show that $\displaystyle b=-tr(A)$ and $\displaystyle c=det(A)$.

I know with a 2x2 matrix that $\displaystyle \lambda^2-tr(A)\lambda+det(A)$ forms the characteristic polynomial; however, I am not sure on how to prove it. I am guessing it is probably trivial if I know that.