3 The cubic equation \(\mathrm { x } ^ { 3 } + \mathrm { cx } + 1 = 0\), where \(c\) is a constant, has roots \(\alpha , \beta , \gamma\).
- Find a cubic equation whose roots are \(\alpha ^ { 3 } , \beta ^ { 3 } , \gamma ^ { 3 }\).
- Show that \(\alpha ^ { 6 } + \beta ^ { 6 } + \gamma ^ { 6 } = 3 - 2 c ^ { 3 }\).
- Find the real value of \(c\) for which the matrix \(\left( \begin{array} { c c c } 1 & \alpha ^ { 3 } & \beta ^ { 3 }
\alpha ^ { 3 } & 1 & \gamma ^ { 3 }
\beta ^ { 3 } & \gamma ^ { 3 } & 1 \end{array} \right)\) is singular.