Matrix to power 30 using eigen values issue 
$$ \text{If matrix } A = \begin{bmatrix} 1 & 0 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 0 \end{bmatrix} \text{ then find } A^{30}.$$

I tried to approach through diagonalization using eigen values method.
I got eigen values as $-1, 1, 1$
As per diagonalization $ A = P*D*P^{-1}.$ So $ A^{30} = P*D^{30}*P^{-1}. $
But $ D^30 = I.$
So, $ A^{30} = P*I*P^{-1} = I $
But $ A^{30} $ is not equal to I. If we do general multiplication without all these. 
Where is the mistake in my approach?

Since $A$ is not diagonalizable we can use Jordan form
\begin{align}
A^{30} &=
\begin{pmatrix}
0 & 2 & 0 \\
-1 & 1 & 1 \\
1 & 0 & 1
\end{pmatrix}
\begin{pmatrix}
-1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 1 & 1
\end{pmatrix}^{30}
\begin{pmatrix}
1/4 & -1/2 & 1/2 \\
1/2 & 0 & 0 \\
-1/4 & 1/2 & 1/2
\end{pmatrix} \\
&=
\begin{pmatrix}
0 & 2 & 0 \\
-1 & 1 & 1 \\
1 & 0 & 1
\end{pmatrix}
\begin{pmatrix}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 30 & 1
\end{pmatrix}
\begin{pmatrix}
1/4 & -1/2 & 1/2 \\
1/2 & 0 & 0 \\
-1/4 & 1/2 & 1/2
\end{pmatrix} \\
&= \begin{pmatrix}
1 & 0 & 0 \\
15 & 1 & 0 \\
15 & 0 & 1
\end{pmatrix}
\end{align}
