I am not sure how to find A^5, can you explain the steps ?

(1 point) Let A be a 3 X 3 diagonalizable matrix whose eigenvalues are 11 = 1, A; = 2, and '13 = 2. If 1 1 0 V1: 0, V2=1, V3=1 0 0 1 are eigenvectors of A corresponding to '11 , '12, and 13, respectively, then factor A into a product PDP'1 with D diagonal, and use this factorization to find A5