How to sequentially add rows to a matrix according to certain contingencies?

The matrix below, allPairs, contains all combinations of pairs of 1, 2, and 3. I want first to permute the rows randomly, as I do using permRows and permAllPairs.

allPairs=[1 1; 2 1; 3 1; 1 2; 2 2; 3 2; 1 3; 2 3; 3 3]
allPairs =

     1     1
     2     1
     3     1
     1     2
     2     2
     3     2
     1     3
     2     3
     3     3

>> permRows=randperm(size(allPairs,1));
>> permRows

permRows =

     6     1     7     4     9     5     8     3     2
permAllPairs = allPairs(permRows(1:9),:)

permAllPairs =

     3     2
     1     1
     1     3
     1     2
     3     3
     2     2
     2     3
     3     1
     2     1

After that, I want to make a new matrix (newPairs) by successively adding each row from permAllPairs into newPairs, according to some rules.

My rules are:

(1) the same row can't be added twice (so if row 3 of permAllPairs, 1,3 was added into newPairs, then 1, 3 can't be added again.)

(2) The flipped row also can't be added. (So if 1, 3 was added, then 3, 1 can't be added to newPairs.)

 If this were to work, I would have a 2x6 matrix, something like FakeNew below.

fakeNew =

     1     1
     3     1
     1     2
     2     2
     2     3
     3     3

I feel like the code that does what I want would be similar in spirit to the terribly wrong code below.

      newPairs=[];

      for i = 1:length(permAllPairs)

          if permAllPairs(i,:) ~= newPairs(i,:) & fliplr(newPairs(i,:))

              newPairs(i,:) == permAllPairs(i,:)
          end
      end
     newPairs

Answer 1

[Andrei Bobrov]

[ii,jj] = ndgrid(1:3);
a = [ii(:),jj(:)];
a1 = a(randperm(length(a)),:);
[b2 b2] = unique(sort(a1,2),'rows');
out = a1(b2,:);

[Molly]

Thank you, very elegant.