Question

A binary operation * is defined on the set R, of real numbers by x*y=3x+3y-xy for all x,y∈R. Determine, in terms of x, the identity element of the operation.

Answer 1

Answer:

Let e be the identity element

Then x*e = e*x = e

Now x*e = e gives

3x + 3e - xe = e

=> xe - 2e = 3x

=> e = 3x /(x-2)

So the required identity element = 3x /(x-2)

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Answer 2

Answer:

The answer is 2

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