$2$ and $0$ are eigenvalues of $\mathbf{T }: \mathbb{ R}^3 \rightarrow \mathbb{ R}^3$ $B=\left\{ \vec{u},\vec{v},\vec{w} \right\}$ is a basis for the transformation and $$E_{2}= Gen\left\{\vec{u}=(1,1,-1)^{T}, \vec{v}=(0,1,-1)^T \right\}$$ $$E_{0}= Gen\left\{\vec{w}=(1,0,-1)^{T}\right\}$$
Then P (The matrix composed by the eigenvectors) is $P=\begin{pmatrix} 1& 0 &1 \\ 1&1 &0 \\ -1& -1 &-1 \end{pmatrix}$ and $P^{-1}=\begin{pmatrix} 1& 1 &1 \\ -1&0 &1 \\ 0& -1 &-1 \end{pmatrix}$ also, by the information given $D=\begin{pmatrix} 2& 0 &0 \\ 0&2 &0 \\ 0& 0 &0 \end{pmatrix}$
Now, I have to find the the matrix associated to the transformation on the basis $B$. I know that $\mathbf{T }(\vec{v})=\lambda(\vec{v})$ but I'm not quite sure of how to proceed.