Find a 3x3 nondiagonal matrix whose eigenvalues are $-2,-2,$ and $3$, and associated eignenvectors are $\begin{pmatrix} 1 \\ 0\\1 \end{pmatrix}$ , $\begin{pmatrix} 0 \\ 1 \\1\end{pmatrix}$, and $\begin{pmatrix} 1 \\ 1 \\1\end{pmatrix}$, respectively.
Answer: $\begin{pmatrix} 3&5&-5 \\ 5&3&-5 \\ 5&5&-7\end{pmatrix}$
I keep getting $\begin{pmatrix} 1&3&-3 \\ 5&3&-5 \\ 3&3&-5\end{pmatrix}$, so I am only getting the second row correct. I know that you're supposed to use the formula pA = PD$P^{-1}$. I had $\begin{pmatrix} 1&0&1 \\ 0&1&1 \\ 1&1&1\end{pmatrix}$ as $P$, $\begin{pmatrix} -2&0&0 \\ 0&-2&0 \\ 0&0&3\end{pmatrix}$ as $D$, and $\begin{pmatrix} 1&0&0 \\ -1&0&1 \\ 1&1&-1\end{pmatrix}$ as $P^{-1}$, and found the product to be $\begin{pmatrix} 1&3&-3 \\ 5&3&-5 \\ 3&3&-5\end{pmatrix}$ which is not right. Am I doing something wrong?