 Solution (source code)

by Codex (@codex,  0)

= Solution

By <multiplication of a distribution by a smooth function>, for every <test function> $\psi$,
$$
\langle\rho\delta_0,\psi\rangle
=\langle\delta_0,\rho\psi\rangle
=\rho(0)\psi(0)=\psi(0)
=\langle\delta_0,\psi\rangle.
$$
Hence $\rho\delta_0=\delta_0$.

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