Use the property of internal energy

Internal energy $U$ is a state function. Therefore, the change in internal energy depends only on the initial and final states, not on the path taken.

Given change from $A$ to $B$

$\Delta U_{A \to B} = U_B - U_A = 40\ \text{kJ mol}^{-1}$

This is true whether the path is reversible or irreversible.

Return from $B$ to $A$

On coming back from $B$ to $A$ by any path (here irreversible), the change in internal energy is:

$\Delta U_{B \to A} = U_A - U_B = -40\ \text{kJ mol}^{-1}$

Net change for the complete cycle

The system goes from $A \to B \to A$, so total change is:

$\Delta U_{\text{net}} = \Delta U_{A \to B} + \Delta U_{B \to A}$

$\Delta U_{\text{net}} = 40 + (-40) = 0$

Conclusion

For a cyclic process, the net change in any state function is zero.

Hence, the correct option is:

$\boxed{\text{C: Zero}}$