[RESOLVED]find nondiagonal matrix whose eigenvalues and eigenvectors are given

Find a 2x2 nondiagonal matrix whose eigenvalues are 2 and -3 and associated eigenvectors are

$\displaystyle \left[ {\begin{array}{c}

-1 \\

2 \\

\end{array} } \right]

$ and $\displaystyle

\left[ {\begin{array}{c}

1 \\

1 \\

\end{array} } \right]$ respectivley.

The answer key has:

Let $\displaystyle D=\left[ {\begin{array}{cc}

2 & 0 \\

0 & -3 \\

\end{array} } \right]

$ and $\displaystyle P=\left[ {\begin{array}{cc}

-1 & 1\\

2 & 1 \\

\end{array} } \right]

$

Then $\displaystyle P^{-1}AP=D$ so $\displaystyle A =PDP^{-1}=\frac{1}{3}

\left[ {\begin{array}{cc}

-4 & -5 \\

-10 & 1 \\

\end{array} } \right]

$

I don't see the intuition behind the first part, how do they know to come up with D and P by slamming together the eigenvectors and eigen values?