10 The matrix \(\mathbf { A }\) is given by \(\mathbf { A } = \left( \begin{array} { r r r } a & 8 & 10
2 & 1 & 2
4 & 3 & 6 \end{array} \right)\). The matrix \(\mathbf { B }\) is such that \(\mathbf { A B } = \left( \begin{array} { l l l } a & 6 & 1
1 & 1 & 0
1 & 3 & 0 \end{array} \right)\).
- Show that \(\mathbf { A B }\) is non-singular.
- Find \(( \mathbf { A B } ) ^ { - 1 }\).
- Find \(\mathbf { B } ^ { - 1 }\).