How to solve 6b?

Question 6. (10 pts) Consider the matrix 0 0 1 A = 1 0 0 0 1 0 (a) (3 pts) Verify that the characteristic polynomial of A is X A (t) = )\\3 + 1. (b) (7 pts) Find a basis of eigenvectors of A. Hint: Note that the 3 distinct roots of X A(t) are 1, a, and a2, where a is the complex number a = 627\"\". The entries of each eigenvector consist of only 1, a and a2 terms