detected field unchanged. An extra minus occurs for the off-diagonal terms, *i.e.*, when swapping a magnetic (electric) detector with an electric (magnetic) source. It is easy to verify that Eq. (\[Eq:reciprocTRANSPOSE\]) is indeed satisfied by the free space Green function $\boldsymbol{G}^0$.

Using this fact, we evaluate Eq. (\[Eq:reciprocTRANSPOSE\]) for the Green function in Eq. (\[Eq:reciprocity\]) to find if reciprocity constrains $\boldsymbol{\alpha}$. Since reciprocity is clearly satisfied for the first term in Eq. (\[Eq:reciprocity\]), we now focus on the second term $$\boldsymbol{G}^0(\bm{r}_2,\bm{r}_s)\boldsymbol{\alpha}\boldsymbol{G}^0(\bm{r}_s,\bm{r}_1)=\boldsymbol{G}^0(\bm{r}_1,\bm{r}_s)
\boldsymbol{\alpha}\boldsymbol{G}^0(\bm{r}_s,\bm{r}_2).
$$ Expanding the matrix products in Eq. (\[Eq:reciprocTRANSPOSE\]) while making use of the reciprocity of the free Green function results in the Onsager relations for the dynamic polarizability: $$\begin{aligned}
\boldsymbol{\alpha}_{EE}=\boldsymbol{\alpha}_{EE}^T,
\quad
\boldsymbol{\alpha}_{HH}=\boldsymbol{\alpha}_{HH}^T,
\quad
 \mbox{and} \quad
\boldsymbol{\alpha}_{EH}=-\boldsymbol{\alpha}_{HE}^T
\qquad
\nonumber \\
 \label{Eq:onsager}\end{aligned}$$ These relations are identical in form to the Onsager relations for constitutive tensors [@Lindell_biisotropicbook], but are now derived on very different grounds for the polarizability of electrodynamically consistent point scatterers. This gratifying result shows that the general point dipoles proposed in this work can be used as microscopic building blocks for an exact scattering theory that describes the formation of bi-anisotropic media from dense lattices of scatterers in the effective medium limit. Indeed, since the point scattering building 