Find a matrix transformation mapping $\{(1,1,1),(0,1,0),(1,0,2)\}$ to $\{(1,1,1),(0,1,0),(1,0,1)\}$ 
Find a matrix transformation mapping $\{(1,1,1),(0,1,0),(1,0,2)\}$ to $\{(1,1,1),(0,1,0),(1,0,1)\}$.

Is the answer 
$$
\begin{bmatrix}1& 0& -1\\0& 1& 1\\0& 0& 1\end{bmatrix}?
$$ 
I understand the concept of Matrix Transformation, I don't think I'm doing it right.

We wish to find a $3\times 3$ matrix $T$ such that $TA=B$ where
\begin{align*}
A &=\begin{bmatrix}1 & 0 & 1\\ 1 & 1 & 0 \\ 1 & 0 & 2 \end{bmatrix}
&
B &= \begin{bmatrix} 1 & 0 & 1\\ 1 & 1 & 0\\ 1 & 0 & 1\end{bmatrix}
\end{align*}
Perhaps the quickest way to find $T$ is to multiply the equation $TA=B$ on the right by $A^{-1}$ to obtain
$$
T=BA^{-1}
$$
Can you compute $A^{-1}$ and carry out the matrix multiplication?
