Determine the numbers a,b if the law of composition x*y=xy+2ax+by is commutative.

Expert Answers

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We have to determine a and b given that for x*y = xy + 2ax + by, the * operator is commutative.

x*y = y*x

=> xy + 2ax + by = yx + 2ay + bx

=> 2ax + by = 2ay + bx

equating the coefficients of x and y we get

2a = b

If the numbers a and b are related as 2a = b, then * is commutative

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