Consider a matrix $P$ and $D$,

$ P =\begin{bmatrix} 8 & 7 \\ 2 & 4 \\\end{bmatrix} $ and $ D =\begin{bmatrix} 6 & 0 \\ 0 & 1 \\\end{bmatrix} $

which are defined as, $ A = PDP^{-1}$. 

To find $ A^{50} $, the equation $ A^{n} = PD^{n}P^{-1} $ is used. 

But since, $ PP^{-1} = I $, shouldn't the equation for finding the $n^{th}$ power of a matrix be simply, $ A^{n} = ID^{n}?$