The binary operation * is defined on the set of R, of real numbers by \(x * y = 3x + 3y - xy, \forall x, y \in R\). Determine, in terms of x, the identity element of the operation.
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Correct Answer: Option A
Explanation:
From the rules of binary operation, \(x * e = x\)
\(\implies x * e = 3x + 3e - xe = x\)
\(3e - xe = x - 3x = -2x\)
\(e = \frac{2x}{x - 3}, x \neq 3\)
From the rules of binary operation, \(x * e = x\)
\(\implies x * e = 3x + 3e - xe = x\)
\(3e - xe = x - 3x = -2x\)
\(e = \frac{2x}{x - 3}, x \neq 3\)