By the Cayley-Hamilton theorem, a matrix $A$ satisfies its own characteristic equation. If $A = \begin{bmatrix} 1 & 2 \\ 0 & 1 \end{bmatrix}$ has characteristic polynomial $p(\lambda) = (\lambda - 1)^2 = \lambda^2 - 2\lambda + 1$, which statement(s) is/are true?