Given the law of composition x*y= xy+4mx+2ny, determine m and n if the law is commutative.

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If an operation % is commutative it implies that x%y = y%x.

As * is commutative for x*y = xy + 4mx + 2ny, we have:

xy + 4mx + 2ny = yx + 4my + 2nx

=> 4mx + 2ny = 4my + 2nx

=> x(2m - n) +...

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If an operation % is commutative it implies that x%y = y%x.

As * is commutative for x*y = xy + 4mx + 2ny, we have:

xy + 4mx + 2ny = yx + 4my + 2nx

=> 4mx + 2ny = 4my + 2nx

=> x(2m - n) + y(n - 2m) = 0

Equating the coefficients of x and y to 0

=> 2m - n = 0 and n - 2m = 0

=> n = 2m

We cannot find an exact value for m and n, we can only say that they are related by the relation n = 2m

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