If A=PDP−1A = PDP^{-1}A=PDP−1 where DDD is diagonal, what is A5A^5A5?
P5D5(P−1)5P^5 D^5 (P^{-1})^5P5D5(P−1)5
PD5P−1P D^5 P^{-1}PD5P−1
D5D^5D5
PDP−1⋅PDP−1⋅…P D P^{-1} \cdot P D P^{-1} \cdot \ldotsPDP−1⋅PDP−1⋅… (5 times)