= Solution
For equal rates, the <change of numeraire> from the Euro bank account to the Dollar account has density process $Z_t=Y_t/Y_0$, a strictly positive mean-one <martingale> under $Q_E$ by part (b). Conditional <change of measure> gives
$$
E_{Q_D}\left[\frac1{Y_t}\mid\mathcal F_s\right]=\frac1{Z_s}E_{Q_E}\left[\frac{Z_t}{Y_t}\mid\mathcal F_s\right]=\frac1{Z_sY_0}=\boxed{\frac1{Y_s}}.
$$
Thus the reciprocal is a genuine <martingale> under $Q_D$, directly from the Euro-measure <martingale> property, without recalculating its stochastic differential equation.
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