Question

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

• A. Closure law
• B. Associative law
• C. Identity law
• D. Inverse law

Answer 1

The correct option is D Inverse law

Given set is $A=\{-1,0,1\}$

1) Closure law :- $-1\times 1=-1\in A;-1\times 0=0\in A,0\times 1=0\in A$

2)Associative law :- $(a\times b)\times c=a\times (b\times c);(-1\times 0)\times 1=0=-1\times (0\times 1)$

3) Identity Law:- $1\in A$

4) Inverse Law :- Inverse of $0$ is not in set $A$

Thus,$A$ does not satifies inverse law.

Hence, $\{-1,0,1\}$ is not a multiplicative group because of the failure of Inverse law.