if I have 
$$
A=
\begin{bmatrix}
\hphantom{-}1 & 0 & 0\\
-1 & 1 & 1 \\
-1 & 0 & 2\\
\end{bmatrix}
$$
I am given the characteristic values are 
$$
\lambda\_{1}=1 \text{ and } \lambda\_{2}=2 
\text{ and A is similar to a characteristic polynomial}
$$
I have found the spectral decomposition of A.
I now need to use this to find 
$$2^{A}$$
how do I do this?