Q97 / 180 · COMEDK 2019 · Mathematics

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

  • A
    Clostre law
  • B
    Associative law
  • C
    Identity law
  • Correct answer
    D
    Inverse law

Solution

We have, $$ A=\{-1,0,1\} $$ Now, let $e$ be the identity element. Then, $\quad a \times e=a \Rightarrow e=1 \in A$ Again, $a^{-1}$ be the inverse element. Then, $\quad a \times a^{-1}=e$ $\Rightarrow \quad a \times a^{-1}=1 \Rightarrow a^{-1}=\frac{1}{a}$ Now, for $a=0, a^{-1}=\frac{1}{0}=\infty \notin A$ So, inverse law fails.

Hence, the correct answer is option: 'D'.

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