Could someone show me how to find the eigenvector of this matrix?
Thanks in advance.
Any will do. (1,0,0), (0,1,0), (0,0,1) form a basis.
Your matrix is the identity matrix. Its characteristic polynomial is , which has three roots, each equal to 1. This is called a degenerate eigenstructure, where every linear combination of -- in this case -- three eigenvectors will have the same eigenvalue.
Hope this helps.