Diagonal Eigenvalue

Question

Consider the matrix $30 \times 30$ matrix $A$ with $A_{ii} = 30$ for $1 \leq i \leq 30$ and $A_{ij} = 1$ for $i \neq j$. Let $\lambda = \begin{bmatrix} \lambda_1 \\ \lambda_2 \end{bmatrix}$ be the vector of distinct eigenvalues $\lambda_1 \neq \lambda_2$ of $A$ and $g = \begin{bmatrix} g_1 \\ g_2 \end{bmatrix}$ be the vector of geometric multiplicities corresponding to $\lambda_1$ and $\lambda_2$, respectively. Find $||\lambda + g||^2$