Hint: Group the P*P^(-1) = I (I is identity matrix) together to get a lot of cancellation and then use A^3 = I to get your final result.
I thought I could not change the order within the multiplication, but so is it that I can do it in thie case? Why?
X^3 = (P^(-1)PA)(P^(-1)PA)(P^(-1)PA)
= P^(-3) (PA)^3
Wait, I did this using laws of indices again, can you please explain how to do it, I'm afraid I do not understand..
Thank you ever so much!