What is a translation property in DFT
The idea is the same as the 1D case. Start with the regular old continuous time fourier transform definition (the integral) and calculate the Fourier transform of $e^{j \omega_0 t} f(t)$. Similarly, calculate the inverse Fourier transform (using the integral) for $e^{j \alpha \omega} F(\omega)$. 

Alternatively, do this with the discrete time fourier transform (so the transform is a sum and the inverse transform is an integral).