A $3 \times 3$ matrix $A$ has trace 9, determinant 24, and two known eigenvalues $\lambda_1 = 2$ and $\lambda_2 = 3$. Find the third eigenvalue $\lambda_3$ and the sum of the principal $2 \times 2$ minors (which equals $\lambda_1\lambda_2 + \lambda_2\lambda_3 + \lambda_1\lambda_3$).