- (i) Prove by induction that for \(n \in \mathbb { Z } ^ { + }\)
$$\left( \begin{array} { r r }
5 & - 1
4 & 1
\end{array} \right) ^ { n } = 3 ^ { n - 1 } \left( \begin{array} { c c }
2 n + 3 & - n
4 n & 3 - 2 n
\end{array} \right)$$
(ii) Prove by induction that for \(n \in \mathbb { Z } ^ { + }\)
$$f ( n ) = 8 ^ { 2 n + 1 } + 6 ^ { 2 n - 1 }$$
is divisible by 7