Solution
= Solution
The <characteristic polynomial> is
$$
\det(tI-A)=\det\begin{pmatrix}t-1&-1\\-1&t\end{pmatrix}=t^2-t-1.
$$
Its two distinct real roots are the <eigenvalues>
$$
\boxed{\varphi=\frac{1+\sqrt5}{2}>0,\qquad \psi=\frac{1-\sqrt5}{2}<0.}
$$
Their product is $-1$, so $\psi=-1/\varphi$. Equivalently, $\varphi^2=\varphi+1$ implies $1/\varphi=\varphi-1$. The positive <eigenvalue> is the <golden ratio>.