The Characteristic Polynomial of a 5 × 5 Matrix Is $$\text { Find a formula for } A ^ { k } \text {, given that } A = P D P - 1 \text {, where } P \text { and } D \text { are given below. }$$

The characteristic polynomial of a 5 × 5 matrix is given below. Find the eigenvalues and their multiplicities.
- $$\text { Find a formula for } A ^ { k } \text {, given that } A = P D P - 1 \text {, where } P \text { and } D \text { are given below. }$$