$_{2}He^{3}$ and $_{1}H^{3}$ nuclei have the same mass number. Do they have the same binding energy?

(B) No,they do not have the same binding energy.
Binding energy depends on the number of protons and neutrons in the nucleus.
For $_{1}H^{3}$ (Tritium),the nucleus consists of $1$ proton and $2$ neutrons.
For $_{2}He^{3}$,the nucleus consists of $2$ protons and $1$ neutron.
The binding energy per nucleon is influenced by the nuclear force,which is attractive between nucleons.
Since $_{1}H^{3}$ has a higher neutron-to-proton ratio and different pairing effects,its total binding energy differs from that of $_{2}He^{3}$.
In general,$_{1}H^{3}$ has a binding energy of approximately $8.48 \text{ MeV}$,while $_{2}He^{3}$ has a binding energy of approximately $7.72 \text{ MeV}$.
Therefore,the binding energies are not the same.