Question 1 - A-Level Maths

1 Let $\mathbf { A } = \left( \begin{array} { l l } 3 & 0
1 & 1 \end{array} \right)$.

Prove by mathematical induction that, for all positive integers $n$, $$2 \mathbf { A } ^ { n } = \left( \begin{array} { l l }