Question

In the group g ={ 1 3 7 9 under multiplication modulo 10 the inverse of 3 is

Answer 1

Answer:

In the group G = {1, 3, 7, 9} under multiplication modulo 10, the inverse of 3 is 10.

Step-by-step explanation:

In any group $(G, \cdot)$, if $1$ is the neutral element of $\cdot$, the inverse of a given element $g \in G$ is an element denoted by $g^{-1}$ such that $g \cdot g^{-1} = g^{-1}\cdot g= 1$.

Note that $3 \cdot 7 = 7\cdot 3 = 21 = 1 \mod(10)$

Then, 7 is the inverse of 3 in $G$.

Answer 2

Answer:

Step-by-step explanation: