How to multiply each elements of single matrix one-by-one?

I have a matrix Xij:

 Xij =[
     0     1    -2     2     6
    -1     0    -3     1     5
     2     3     0     4     8
    -2    -1    -4     0     4
    -6    -5    -8    -4     0];

I need to multiply each elements of this matrix with each elements of this matrix again. For example, I need to multiply X13*X24 or X12*X24. And I need to multiply for all matrix.

I have tried the code below, but it multiplies just X11*X11 (like square):

 Xij =[
     0     1    -2     2     6
    -1     0    -3     1     5
     2     3     0     4     8
    -2    -1    -4     0     4
    -6    -5    -8    -4     0];
 for m=1:5
 for n=1:5
    A(m,n)=Xij(m,n)*Xij(m,n);
 end
 end

I got unnecessary result like:

 A =
     0     1     4     4    36
     1     0     9     1    25
     4     9     0    16    64
     4     1    16     0    16
    36    25    64    16     0

Could anyone help me, please?

Answer 1

[James Tursa]

This will multiply every element by every other element:

result = Xij(:) * Xij(:)';  % <-- Simple outer product of all the elements

If you want the resulting elements to be in a specific order, or the size of the result to be in a specific shape, please specify.