The set of integers $Z$ with the binary operation $$ defined as $a b = a + b + 1$ for $a, b, Z$ is a group. The identity element of this group is

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Solution

The correct option is C $- 1$
$a * b = a + b + 1$ (a,b,z is a group)
at $a = - 1 \Rightarrow a * b = - 1 + b + 1 = b$
at $b = - 1 \Rightarrow a * b = a - 1 + 1 = a$
$\Rightarrow a * 0 = a + 0 + 1$
$\Rightarrow$ identity element is $- 1$ .

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The set of integers Z with the binary operation ∗ defined as a∗b=a+b+1 for a,b,Z is a group. The identity element of this group is

The correct option is C −1a∗b=a+b+1 (a,b,z is a group)at a=−1⇒a∗b=−1+b+1=bat b=−1⇒a∗b=a−1+1=a⇒a∗0=a+0+1⇒ identity element is −1.

The set of integers $Z$ with the binary operation $$ defined as $a b = a + b + 1$ for $a, b, Z$ is a group. The identity element of this group is

The correct option is C $- 1$
$a * b = a + b + 1$ (a,b,z is a group)
at $a = - 1 \Rightarrow a * b = - 1 + b + 1 = b$
at $b = - 1 \Rightarrow a * b = a - 1 + 1 = a$
$\Rightarrow a * 0 = a + 0 + 1$
$\Rightarrow$ identity element is $- 1$ .