Diagonalization & Matrix Powers · Hard problem

A $3\times 3$ matrix $A$ has eigenvalue $1$ with eigenvector $(1, 0, 1)$, eigenvalue $-1$ with eigenvector $(1, 1, 0)$, and eigenvalue $0$ with eigenvector $(0, 1, 1)$. Find the entry in row 1, column 2 of $A^{2025}$.