Let $L\colon M_{2 \times 3} \to M_{3 \times 3}$ be the linear transformation defined by $L(A) = \left[\begin{array}{rr}2 & -1 \\ 1 & 2 \\ 3 & 1\end{array}\right]\,A$. Find the dimension of the range of $L$.
Answer: $6$
How is the answer $6$? Isn't it $2$?