2 \times 3 ^ { n } & 0
3 ^ { n } - 1 & 2 \end{array} \right)$$ (b) Find, in terms of \(n\), the inverse of \(\mathbf { A } ^ { n }\).
2 The cubic equation \(x ^ { 3 } + 4 x ^ { 2 } + 6 x + 1 = 0\) has roots \(\alpha , \beta , \gamma\).
(a) Find the value of \(\alpha ^ { 2 } + \beta ^ { 2 } + \gamma ^ { 2 }\).
(b) Use standard results from the list of formulae (MF19) to show that $$\sum _ { r = 1 } ^ { n } \left( ( \alpha + r ) ^ { 2 } + ( \beta + r ) ^ { 2 } + ( \gamma + r ) ^ { 2 } \right) = n \left( n ^ { 2 } + a n + b \right)$$ where \(a\) and \(b\) are constants to be determined.