Lets work over $\mathbb{C}$. Let $G$ be a reductive group with semisimple rank 1 (this means that a maximal torus in $G / R(G)$ has dimension 1). In section 25 of Humphreys book "linear algebraic groups", it is claimed that $G / Z(G)$ is isomorphic to ${\rm PGL}_2$, but I don't understand the proof.

Lets work over $\mathbb{C}$. Let $G$ be a reductive group with semisimple rank 1 (this means that a maximal torus in $G / R(G)$ has dimension 1). In section 25 of Humphreys book "linear algebraic groups", it is claimed that $G / Z(G)$ is isomorphic to ${\rm PGL}_2$, but I don't understand the proof. Let me be a little more precise. Write $I$ for the intersection of all borel subgroups of $G$. I understand why $ G / I \cong {\rm PGL}_2$ and why $I / Z(G)$ is finite. I just don't understand how Humphreys concludes that $I = Z(G)$.