Chapter 6.4, Problem 14P

For Problems $10-14$, find $\text{Ker}\left(T\right)$ and $\text{Rng}\left(T\right)$, and hence, determine whether the given transformation is one-to-one, onto, both, or neither. If $T^{-1}$ exists, find it.

$T\left(x\right)=Ax$, where $A=\left[\begin{array}{ccc}0& 1& 2\\ 3& 4& 5\\ 5& 4& 3\\ 2& 1& 0\end{array}\right]$.