Eigenvalue statements help

1. Dec 4, 2009

Whiz

1. The problem statement, all variables and given/known data

Let A and B be n x n matrices, where B is invertible. Suppose that 2 is an eigenvalue of A, and −2 is an eigenvalue of B. Find ALL true statements below.

A. −4 is an eigenvalue of AB
B. 16 is an eigenvalue of A^3+A+6I
C. 4 is an eigenvalue of A+A(Transpose)
D. 2 is an eigenvalue of A(Transpose)
E. 2 is an eigenvalue of B^(−1)AB
F. None of the above

3. The attempt at a solution

I'm not sure how to do this question, so can anyone show me the correct way to solve this?
I picked 2 random matrices for A and B that fit the given description and tried all of the operations. Only A,B,D,E worked, but it's the wrong answer.

Can anyone help me?

Thanks.

Last edited: Dec 4, 2009
2. Dec 4, 2009

lanedance

Re: Eigenvalues

see if these help
A) can you think of a counter example with diagonal matricies?
B,C,D) try writing the determinsitic equation and see what you get...
E) do you know about similar matricies?