Question

multiplicative inverse of 3 in z5​

Answer 1

Answer:

z5 in 3 is multiplicative inverse according to me

Answer 2

The multiplicative inverse of 3 in Z₅ is 2

Given :

The group Z₅

To find :

The multiplicative inverse of 3 in Z₅

Solution :

Step 1 of 2 :

Write down the given group

Here the given group is Z₅

1 is multiplicative identity

Step 2 of 2 :

Find multiplicative inverse of 3 in Z₅

Let x ∈ Z₅ be the multiplicative inverse of 3 in Z₅

Then from definition of multiplicative inverse we get ,

$\displaystyle \sf{ 3.x \equiv 1(mod \: 5)}$

$\displaystyle \sf{ \implies 3x \equiv \: 1(mod \: 5)}$

Thus holds only when x = 2

Hence the multiplicative inverse of 3 in Z₅ is 2

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