Help with Linear Algebra(Eigenvalues)

I'm having trouble with a few of the harder linear algebra concepts from the eigenvalue chapter.
1) Using the matrix A= | 3 -2 |
| 1 2 |
verify the Cayley Hamilton theorem.

2) Given the rotation matrix Rtheta = | cos -sin|
| sin cos|
show the matrix has eigenvectors and eigenvalues corresponding to
lambda= e^i*theta : |1|
|-i|
lambda= e^-i*theta |1|
|i |
3)Show that similar matrices A and B have the same eigenvalues. Thus you must show that det(A-lambda*I)= det(B-lambda*I)

Thanks to anyone takes a look at this.
Edit/Delete Message

I'm not saying google should become your best fried but at least make it one of your friends:

Cayley–Hamilton theorem - Wikipedia, the free encyclopedia

Eigenvalue, eigenvector and eigenspace - Wikipedia, the free encyclopedia

3. if A and B are similar then there exists and invertible mtrix P such that: