Using the result
$$( \mathbf { A B } ) ^ { \mathrm { T } } = \mathbf { B } ^ { \mathrm { T } } \mathbf { A } ^ { \mathrm { T } }$$
show that
$$\left( \mathbf { A } ^ { - 1 } \right) ^ { \mathrm { T } } = \left( \mathbf { A } ^ { \mathrm { T } } \right) ^ { - 1 }$$
8
It is given that \(\mathbf { A } = \left[ \begin{array} { c c } 4 & 5 - 1 & k \end{array} \right]\), where \(k\) is a real constant.
8
Find \(\left( \mathbf { A } ^ { - 1 } \right) ^ { \mathrm { T } }\), giving your answer in terms of \(k\)
8
(ii) State the restriction on the possible values of \(k\)