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.