We can then use this relation to rewrite the reduced matrix element containing the position vector as $$ \begin{eqnarray*} \langle l \vert\vert\left[{\bf r} \otimes {\bf r} \right]^{(2)} \vert \vert l'\rangle & = & \sqrt{4\pi}\sqrt{ \frac{2}{15}}r^2 \langle l \vert\vert Y_2 \vert \vert l'\rangle \\ & = &\sqrt{4\pi}\sqrt{ \frac{2}{15}} r^2 (-1)^l \sqrt{\frac{(2l+1)5(2l'+1)}{4\pi}} \left(\begin{array}{ccc} l&2&l' \\ 0&0&0\end{array}\right) \end{eqnarray*} $$