Help finding the eigenvalues of a matrix

Hey! So I have a question on an assignment asking to orthogonally diagonalize the matrix:
a 0 b
0 a 0
b 0 a
I know the steps on how to do this, but am having a hard time trying to figure out how to factor this correctly to get all of the eigenvalues at the beginning. I can factor it to a point, but then cannot seem to figure out how to solve for the eigenvalues.

If anyone could help, that would be great!

Have a look here

http://www.mathhelpboards.com/f14/sarah-morashs-question-yahoo-answers-about-eigenvalues-3203/#post14133

I hope this helps.