MATLAB: Define new operations for a matrix

cummutativeinterp2interpolationmultiplicationnew operationstimes table

I have 2 vectors x=[0 1 2 0 1 0 3 1 0] and its transposed column vector y=x'
I need to define a new operation , let's say * following the multiplication table underneath
0 1 2 3
1 0 3 2
2 3 0 1
3 2 1 0
For instance under this new * commutative operation
0*1=1*0=1
1*1=0 or
3*2=1 or 2*3=1 or
3*3=0
And I would like to build a matrix A having first row x and first column y where the elements of the matrix would be each the result of individual element x.*y or y.*x but using only vectors x and y and defining the new operation * .
The result should be
A=[0 1 2 0 1 0 3 1 0; 1 0 3 1 0 1 2 0 1; 2 3 0 2 3 2 1 3 2; 0 1 2 0 1 0 3 1 0;1 0 3 1 0 1 2 0 1;0 1 2 0 1 0 3 1 0; 3 2 1 3 2 3 0 2 3;1 0 3 1 0 1 2 0 1;0 1 2 0 1 0 3 1 0]
A =
0 1 2 0 1 0 3 1 0
1 0 3 1 0 1 2 0 1
2 3 0 2 3 2 1 3 2
0 1 2 0 1 0 3 1 0
1 0 3 1 0 1 2 0 1
0 1 2 0 1 0 3 1 0
3 2 1 3 2 3 0 2 3
1 0 3 1 0 1 2 0 1
0 1 2 0 1 0 3 1 0

Best Answer

x = [0,1,2,0,1,0,3,1,0];
y = x.';
V = 0:3; % define value range of multiplication table
M = [0,1,2,3;1,0,3,2;2,3,0,1;3,2,1,0] % define multiplication table
M = 4×4
     0     1     2     3
     1     0     3     2
     2     3     0     1
     3     2     1     0

A = interp2(V,V,M,x,y)
A = 9×9
     0     1     2     0     1     0     3     1     0
     1     0     3     1     0     1     2     0     1
     2     3     0     2     3     2     1     3     2
     0     1     2     0     1     0     3     1     0
     1     0     3     1     0     1     2     0     1
     0     1     2     0     1     0     3     1     0
     3     2     1     3     2     3     0     2     3
     1     0     3     1     0     1     2     0     1
     0     1     2     0     1     0     3     1     0

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