A = [1 2;
     3 4];

B = [5 6;
     7 8];

C = [A B;
     B A];

%so that:
C = [1 2 5 6;
     3 4 7 8;
     5 6 1 2;
     7 8 3 4];

C = [A B A;
     B A B;
     A B A];

C = [A B A B;
     B A B A;
     A B A B;
     B A B A];

function [C] = matrices(x)

A = [1 2; 3 4];
B = [5 6; 7 8];

%Determine size N of matrix.
N = size(A,1);

%Assign passed argument to M.
M = x;

%mod operator to determine odd or even M.
if(~mod(M,2))
    %concatenate A and B and repeat matrix
    C = repmat([cat(2,[A B]);cat(2,[B A])],M/2);
else
    %concatenate A and B and repeat matrix
    C = repmat([cat(2,[A B]);cat(2,[B A])],(M+1)/2);
    %remove additional rows and columns created by matrix repetition
    C = C(:,1:end-N);
    C = C(1:end-N,:);
end
end

D =  [1     2     5     6
      3     4     7     8
      5     6     1     2
      7     8     3     4]

D =  [1     2     5     6     1     2
      3     4     7     8     3     4
      5     6     1     2     5     6
      7     8     3     4     7     8
      1     2     5     6     1     2
      3     4     7     8     3     4]

D = [1     2     5     6     1     2     5     6
     3     4     7     8     3     4     7     8
     5     6     1     2     5     6     1     2
     7     8     3     4     7     8     3     4
     1     2     5     6     1     2     5     6
     3     4     7     8     3     4     7     8
     5     6     1     2     5     6     1     2
     7     8     3     4     7     8     3     4]