During expansion of a gas into vacuum ($P_{ext}=0$), work done is zero if the process is 

A) Reversible B) Irreversible C) Isothermal 

In isothermal process, the temperature $T$ is constant and pressure $P$ is inversely proportional to the volume, $V$

$\frac{P_2}{P_1}=\frac{V_1}{V_2}$ and in vacuum it is zero. So work done is also zero.

In an irreversible process, work done $=-P_{\text{ext }}{d}_x$ and in vacuum it is zero so, the work done is zero.

A reversible process is known as a cyclic process.

Hence, during free expansion of an ideal gas no work is done and $P_{\text{ext }}=0$ in a vacuum.

So, this process is reversible, irreversible and isothermal.

Therefore, option (A) is correct.