Let

$ E $ - Elliptic curve defined over $ {\mathbb{Q}} $.

$G_{\mathbb{Q}}$ - The absolute Galois group, $\text{Gal}(\bar{\mathbb{Q}}/\mathbb{Q}) $ of $\mathbb{Q}$.

$ E[3] $ - $3$-torsion points of $ E $.

Suppose $ \rho$ denotes the $ G_{\mathbb{Q}} $-representation associated to $ E[3]$. If $ E $ has a $3$-torsion point over $ \mathbb{Q} $, how to prove $$ \rho \sim \left( {\begin{array}{cc} 1 & \eta \\ 0 & \chi \\ \end{array} } \right) $$ where $ \chi $ is the mod 3 cyclotomic character $?$