Chapter 6.4, Problem 3P

Let $T_1:{ℝ}^2\to {ℝ}^3$ and $T_2:{ℝ}^3\to {ℝ}^2$ be the linear transformations with matrices

$A=\left[\begin{array}{cc}2& -1\\ 0& 1\\ 1& 1\end{array}\right]$, $B=\left[\begin{array}{ccc}0& -4& 3\\ 1& 0& 1\end{array}\right]$, respectively. Find $T_1{T}_2$, $\text{Ker}\left(T_1{T}_2\right)$, $\text{Rng}\left(T_1{T}_2\right)$, $T_2{T}_1$, $\text{Ker}\left(T_2{T}_1\right)$, and $\text{Rng}\left(T_2{T}_1\right)$