The cubic equation \(x^3 + 5x^2 + 10x - 2 = 0\) has roots \(\alpha, \beta, \gamma\).

(a) Find the value of \(\alpha^2 + \beta^2 + \gamma^2\).

(b) Show that the matrix \(\begin{pmatrix} 1 & \alpha & \beta \\ \alpha & 1 & \gamma \\ \beta & \gamma & 1 \end{pmatrix}\) is singular.