Question: How to list all cases of Reynolds operator?

for simple case 2*2,  A = matrix([[0,-1],[1,0]]);

using A, i understand f(x,y) = f(-y,x)

where do other case f(-x,-y) and f(y,-x) come from?

any command to list all cases with input a matrix A?

if A has more dimensions, what will the cases be ?

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