Question:
In the group $(R-\{-1\}, *)$ where $*$ is defined by $a*b = a+b+ab, \forall a,b \in R-\{-1\}$, inverse of the element 2 is}
In the group $(R-\{-1\}, *)$ where $*$ is defined by $a*b = a+b+ab, \forall a,b \in R-\{-1\}$, inverse of the element 2 is}
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Always find the identity ($e$) first; the inverse is the value that "undoes" the element to get back to $e$.
Updated On: Jul 3, 2026
- $\frac{1}{2}$
- $-\frac{2}{3}$
- $-\frac{3}{2}$
- $-\frac{1}{2}$
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The Correct Option is B
Solution and Explanation
Step 1: Concept
To find the inverse, first find the identity element $e$ such that $a*e = a$. Then find $b$ such that $a*b = e$.
Step 2: Meaning
$a+e+ae = a \Rightarrow e(1+a) = 0 \Rightarrow e = 0$. The identity element is 0.
Step 3: Analysis
To find the inverse of 2, set $2*b = 0 \Rightarrow 2+b+2b = 0$.
Step 4: Conclusion
$2 + 3b = 0 \Rightarrow 3b = -2 \Rightarrow b = -2/3$. The inverse of 2 is $-2/3$. Final Answer: (B)
To find the inverse, first find the identity element $e$ such that $a*e = a$. Then find $b$ such that $a*b = e$.
Step 2: Meaning
$a+e+ae = a \Rightarrow e(1+a) = 0 \Rightarrow e = 0$. The identity element is 0.
Step 3: Analysis
To find the inverse of 2, set $2*b = 0 \Rightarrow 2+b+2b = 0$.
Step 4: Conclusion
$2 + 3b = 0 \Rightarrow 3b = -2 \Rightarrow b = -2/3$. The inverse of 2 is $-2/3$. Final Answer: (B)
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