Question

Find the multiplicative inverse of 8 mod 11

Answer 1

Answer:

1. 1 = 11(3) - 8(4).
2. The goal is to find a multiplicative inverse for 8 (mod 11), meaning you want to find an integer n such that 8n = 1 (mod 11).
3. Consider the equation above, and reduce it modulo 11. Since
4. 11(3) = 0(3) = 0 (mod 11),
5. you thus get
6. 11(3) - 8(4) = 8(-4) = 1 (mod 11).
7. This means that -4 is a multiplicative inverse for 8, modulo 11, not 4.
8. To get something more compatible with your answer key, knowing that -4 is a multiplicative inverse modulo 11, what's a positive integer n satisfying 8n = 1 (mod 11)?

          I hope this helps.

Answer 2

Concept:

Multiplicative inverse means when a number is multiplied with the inverse than the answer is 1.

multiplicative inverse is one of the properties of multiplication.

Given:

we are given the expression:

8|11|

Find:

We need to find the multiplicative inverse of the expression given .

Solution:

To find the multiplicative inverse, we will first write the expression as:

1=11(3)-8(4)

8n=|11|

From this, we get that the multiplicative inverse of the expression given is-4.

Therefore, we get that the multiplicative inverse is - 4 for the given expression.

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