For a square matrix $A$, fundamental relationships include: $\text{tr}(A) = \sum_{i} \lambda_i$ (sum of eigenvalues), $\det(A) = \prod_i \lambda_i$ (product of eigenvalues), and $\text{tr}(A^k) = \sum_i \lambda_i^k$. For $A = \begin{pmatrix} 1 & 2 \\ 3 & 5 \end{pmatrix}$, which statement is FALSE?