2.
$$\mathbf { A } = \left( \begin{array} { r r r }
- 1 & 3 & a
2 & 0 & 1
1 & - 2 & 1
\end{array} \right) , \quad \mathbf { B } = \left( \begin{array} { r r r }
2 & 0 & 4
3 & - 2 & 3
1 & 2 & b
\end{array} \right)$$
where \(a\) and \(b\) are constants.
- Write down \(\mathbf { A } ^ { \mathrm { T } }\) in terms of \(a\).
- Calculate \(\mathbf { A B }\), giving your answer in terms of \(a\) and \(b\).
- Hence show that
$$( \mathbf { A B } ) ^ { \mathrm { T } } = \mathbf { B } ^ { \mathrm { T } } \mathbf { A } ^ { \mathrm { T } }$$