Question

1.
If A= {0,1, -1}, check whether (A, +) and ( A, x) are groups or not​

Answer 1

Answer:

$(A,\times)$ is not a group

Step-by-step explanation:

A= {0,1, -1}

1.clearly A is closed under addition

2.Usual addition is always associative

3. identity element $0\in\:A$ and satisfies a+0=0+a=a for all $a\in\:A$

4.

Inverse of 0 is 0

Inverse of 1 is -1

Inverse of -1 is 1

Inverse axiom is true

Hence (A,+) is a Group

1.clearly A is closed under multiplication

2.Usual multiplication is always associative

3. identity element $1\in\:A$ and satisfies $a\times\:1=1\times\:a=a for all [tex]a\in\:A$

4.

Inverse axiom is not true because inverse of 0 does not exist

Hence $(A,\times)$ is not a Group