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The binary operation $\square$ is defined as $a\square b = ab+(a+b),$ where $a$ and $b$ are any two real numbers. The value of the identity element of this operation, defined as the number $x$ such that $a\square x = a,$ for any $a$, is 

  1. $0$
  2. $1$
  3. $2$
  4. $10$
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Given that $:a\square b=ab+(a+b)$

Identity element of this operation, defined as the number $x$ such that $a\square x = a$

$\implies ax+(a+x) = a$

$\implies ax+x=0$

$\implies x(a+1)=0$

$\implies x =0,a=-1\in \mathbb{R}$

So, the correct answer is $(A).$
Answer:

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