Thanks to all in advance for looking at this problem.

Given A is an unspecified 3 x 3 matrix that has eigenvlaues 2, -2, square root of 3 and the corresponding eigenvectors are X1, X2, X3.

a) Find the characteristic polynomial of A.

b) Find a set of three linearly independent eigenvectors of A^2

c) Find the characteristic polynomial of A^2