Let $T\colon M_{23} \to M_{33}$ be the linear transformation defined by $T(A)=\begin{pmatrix} 2 & -1 \\ 1 & 2 \\ 3&1 \end{pmatrix}\,A$, for $A\in M_{23}$. Find a basis for the kernel and range of $T$.
I don't know how to exactly approach this question. All I know is that the kernel of $T$ would be the nullspace. I row reduced $\begin{pmatrix} 2 & -1 \\ 1 & 2 \\ 3&1 \end{pmatrix}$ and got $\begin{pmatrix} 1 & 0 \\ 0 & 1 \\ 0&0 \end{pmatrix}$ but I don't know what to do from here.