$\displaystyle A:\mathbb{R}_{2}[x]->\mathbb{R}^{3} , A(P)=(P(-1),P(0),P(1))$

where A is a bijective linear transformation, $\displaystyle \mathbb{R}_{2}[x]$ is the set of polynomials with real coeficients and max degree=2 .

Find $\displaystyle A^{-1}(0,6,0)$

To do this I have to find the matrix of A relative to canonical basis of $\displaystyle \mathbb{R}_{2}[x]$ and $\displaystyle \mathbb{R}^{3}$ , find the inverse of that matrix and then $\displaystyle A^{-1}\begin{pmatrix}0\\ 6\\ 0\end{pmatrix}$ is the answer I'm looking for.

Please tell me if I am right or not.