Eigenvalues · Challenge problem

Let $A = \begin{pmatrix}1 & 2 & 3\\4 & 5 & 6\\7 & 8 & 10\end{pmatrix}$ have eigenvalues $\lambda_1, \lambda_2, \lambda_3$. Find $\lambda_1\lambda_2 + \lambda_1\lambda_3 + \lambda_2\lambda_3$.