Matching two matrices by row but allowing for permutations

I'm having some questions about a simple strategy to rearrange two matrices such that their rows match up. Normally I would not ask immediately but I tried searching without avail, unless I haven't gone far enough.

I'm basically trying to match two matrices row-by-row, but the twist is that for the matrix to be rearranged, we only know that for each row in the target matrix, there exists a row in the candidate matrix that shares all elements. For example, we can have this:

A = [16 2;
    3 13;
    5 11;
    10 8;
    9 7;
    6 12;
    4 14;
    15 1;]

B = [1 15;
    7 9;
    4 14;
    16 2;
    13 3;
    5 11;
    10 8;
    12 6;]

What operation need we impose on B to match A? It is clear that there are matching rows, but not only are the rows themselves out of order, the elements within each row are also permuted.

Answer 1

[Matt J]

the elements within each row are also permuted.

Well, they don't have to stay that way, do they?

A=sort(A,2)
B=sort(B,2)

Now you can find corresponding row indices using ismember,

[~,loc]=ismember(B,A,'rows')