Permute/Re​arrange/Sh​uffle the elements of a matrix

Hi, I have

 A=[2     3
    4     1
    1     4
    3     2
    5     5];

I want have the all possible arrangements, with a condition,there is no repetition for each column.

How can I do this? Thanks in advance.

[Geoff Hayes]

Grace - so you want all 5x2 matrices which have elements 1 through 5 in each column arranged uniquely? Or are the rows fixed and you want all arrangements of the rows? Please provide some of the arrangements from your above example or start with a smaller matrix to make it more clear what you expect.

[Grace]

Hi Geoff, yes, I want all 5x2 matrices have elements 1 through 5 in each column arranged uniquely.

Let's take a smaller matrix as an example:

 B=[1 1; 
   2 2]

The matrix above contains 2 rows, the elements are 1 and 2.

The possible arrangements for B are

 B1=[1 2; 
     2 1]

 B2=[2 2; 
     1 1]

 B3=[2 1; 
     1 2]

The arrangements like

 [1 1; 
  1 2]

or

 [1 2; 
 1 2]

which contain repeated elements for each column are not the arrangements that i wish to get.

Answer 1

[Roger Stafford]

With n = 5 rows in A you would get 14,400 different B matrices and that is too many to dream up names for, so I have put them all into a single n-by-2-by-(n!)^2 array which I call B. Each slice along the third dimension would be one of your n-by-2 matrices which you called B1, B2, B3, etc.

 n = size(A,1);
 P = perms(1:n)';
 N = size(P,2);
 B = zeros(n,2,N,N);
 for i1 = 1:N
   for i2 = 1:N
     B(:,:,i1,i2) = [A(P(:,i1),1),A(P(:,i2),2)];
   end
 end
 B = reshape(n,2,N^2);

[Grace]

Hi Roger, I can't understand the reshape part, and the output shows me:

 >> Untitled
Error using reshape
To RESHAPE the number of elements must not
change.

 Error in Untitled (line 42)
 B = reshape(n,2,N^2)