6 You are given that \(\mathbf { A } = \left( \begin{array} { l l } 1 & a
0 & 1 \end{array} \right)\) where \(a\) is a constant.
Prove by induction that \(\mathbf { A } ^ { \mathrm { n } } = \left( \begin{array} { c c } 1 & \text { an }
0 & 1 \end{array} \right)\) for all integers \(n \geqslant 1\).