Question

In the group $G = \{0,1,2,3,4\}$ under $\times_5$, the inverse of $(2 \times_5 2^{-1})$ is}

• A. 0
• B. 1
• C. 2
• D. 3

Hint:

In any group, $a \cdot a^{-1} = e$ and the inverse of the identity is the identity itself.

Answer 1

The Correct Option is B

Step 1: Conceptual Understanding:
$a \times a^{-1} = e$ (the identity element).
Step 2: Explanation in Detail:
$2 \times_5 2^{-1} = e = 1$ (the identity under $\times_5$).
The inverse of the identity element is the identity itself: $e^{-1} = e = 1$.
Step 3: Therefore, Stating the Final Answer
The inverse of $2 \times_5 2^{-1}$ is $1$.