How to calculate Discrete Fourier transform of a matrix by numerically?

Here I am able write code to find out DFT of array numerically with out using for loop(2 nd for loop), I am facing problem to find out DFT by using 2 for loop in following code, in place of 0 1 2 3, I have to use for loop. How to extend this 1D DFT to find out DFT of matrix. Example matrix A=[3 4;5 6]

clear all;

clc;

close all;

x=[24 8 12 16];

A=0;

B=0;

C=0;

D=0;

for xi=1:1:4

A=A+1/4*(x(xi)*exp(-1i*2*pi*(xi-1)*0/4));

B=B+1/4*(x(xi)*exp(-1i*2*pi*(xi-1)*1/4));

C=C+1/4*(x(xi)*exp(-1i*2*pi*(xi-1)*2/4));

D=D+1/4*(x(xi)*exp(-1i*2*pi*(xi-1)*3/4));

end

E=[A B C D]

Thank you very much for this kind help in advance

Yours

Mohd abdul Gaffar