Modulation index, $m=\frac{\mathrm{Peak} \mathrm{value} \mathrm{of} \mathrm{modulating} \mathrm{signal}\left(E_m\right)}{\mathrm{Peak} \mathrm{value} \mathrm{of} \mathrm{carrier} \mathrm{signal}\left(E_c\right)}$

When modulating signal is increased by $1\%$, then, $E_m^{\text{'}}=\left(1+0.01\right)E_m=1.01E_m$

And when carrier signal in increased by $3\%$, then, $E_c^{\text{'}}=\left(1+0.03\right)E_c=1.03E_c$

Now, the new modulation index is $m^{\text{'}}=\frac{1.01E_m}{1.03E_c}=0.98m$

Thus, the modulation index changes by $-2\%$.