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JEE Advanced
Exam
JEE Advanced
Subject
Mathematics
Chapter
Sets and Relations

JEE Advanced · Mathematics · Sets and Relations

The set \ -1,0,1\ is not a multiplicative group because of the...

The set {−1,0,1}\{-1,0,1\} is not a multiplicative group because of the failure of

Options

  1. AClostre law
  2. BAssociative law
  3. CIdentity law
  4. DInverse law

Correct answer

D. Inverse law

Step-by-step solution

We have,

A=\{-1,0,1\}

Now, let ee be the identity element. Then, a×e=a⇒e=1∈A\quad a \times e=a \Rightarrow e=1 \in A Again, a−1a^{-1} be the inverse element. Then, a×a−1=e⇒a×a−1=1⇒a−1=1a\quad a \times a^{-1}=e\Rightarrow \quad a \times a^{-1}=1 \Rightarrow a^{-1}=\frac{1}{a}
Now, for a=0,a−1=10=∞∉Aa=0, a^{-1}=\frac{1}{0}=\infty \notin A
So, inverse law fails.
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