COMEDK · Maths · 17. Mathematical Reasoning
In the group \(Q-\{1\}\) under the binary operation * defined by \(a * b=a+b+a b\) the inverse of 10 is
- A \(\frac{1}{10}\)
- B \(\frac{11}{10}\)
- C \(\frac{-11}{10}\)
- D \(\frac{-10}{11}\)
Answer & Solution
Correct Answer
(D) \(\frac{-10}{11}\)
Step-by-step Solution
Detailed explanation
Let the inverse element of 10 be \(e\), then \[ a * e=0 \] Therefore, \(10 \div e=10+e+10 e=0\) \[ \Rightarrow \quad 10+11 e=0 \] \(\begin{array}{rr}\Rightarrow & 11 e=-10 \\ \Rightarrow & e=\frac{-10}{11}\end{array}\)
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