According to the first law of thermodynamics, the heat supplied to a system ($\Delta Q$) is equal to the sum of the increase in internal energy ($\Delta U$) and the work done by the system ($\Delta W$). This is expressed as $\Delta Q = \Delta U + \Delta W$. In an adiabatic process, there is no heat exchange between the system and its surroundings, which means $\Delta Q = 0$. Substituting this into the first law equation, we get $0 = \Delta U + \Delta W$, which simplifies to $\Delta U = -\Delta W$. For an isothermal process, the temperature remains constant, so the change in internal energy for an ideal gas is zero ($\Delta U = 0$), making $\Delta Q = \Delta W$. Thus, the only correct statement is option A.