DFT of a 2-D image using matrix multiplication

clc; clear all;
%x = [0 1 2 1; 1 2 3 2; 2 3 4 3; 1 2 3 2];
x = double(imread('cameraman.tif'));
n = length(x);

DFT_matrix = exp(-2i * pi / n * [0:n-1]' * [0:n-1])
%DFT_matrix = [1 1 1 1; 1 -i -1 i; 1 -1 1 -1; 1 i -1 -i];

step1=zeros(n);
for i=1:n %Row multiplications
    step1(i, :) = DFT_matrix*x(i, :)';
end

step2=zeros(n);
for i=1:n %Col multiplications
   step2(:, i) = DFT_matrix*Step1(:,i);
end

figure(1), imshow(uint8(x));
figure(2), imshow(uint8(Step2));