Table of Contents

## How do you find the inverse of a modulo?

A naive method of finding a modular inverse for A (mod C) is:

- Calculate A * B mod C for B values 0 through C-1.
- The modular inverse of A mod C is the B value that makes A * B mod C = 1. Note that the term B mod C can only have an integer value 0 through C-1, so testing larger values for B is redundant.

### What is the inverse of 7 modulo 11?

7x≡1≡12≡23≡34≡45≡56(mod11). Then from 7x≡56(mod11), we can cancel 7, obtaining x≡8(mod11). Hence, −3 is the inverse of 7(mod11).

**What is the multiplicative inverse of 5 under modulo 13?**

Thus, the multiplicative inverse of 5 modulo 13 is -5, or equivalently 13–5 = 8.

**What is the inverse of 2 modulo 17?**

Therefore −8 is an inverse of 2 mod 17. Note that −8+17=9 is also an inverse of 2 mod 17, as is −8+2 · 17 = 26, etc.

## How do you find the inverse of a matrix mod 26?

For a matrix to have an inverse modulo 26, the determinant of the matrix must be 1,3,5,7,9, 11, 15, 17, 19, 21, 23, or 25 modulo 26. To be able to undo multiplication by a matrix modulo 26, the determinant of the matrix must be 1,3,5,7,9, 11, 15, 17, 19, 21, 23, or 25 modulo 26.

### How do I find the inverse of a number?

For the multiplicative inverse of a real number, divide 1 by the number. For example, the reciprocal of 5 is one fifth (1/5 or 0.2), and the reciprocal of 0.25 is 1 divided by 0.25, or 4.

**How do you find the inverse of a 2×2 matrix mod 26?**

2×2 matrix is just the product down the upper left to lower right diagonal minus the product down the upper right to lower left diagonal. For a matrix to have an inverse modulo 26, the determinant of the matrix must be 1,3,5,7,9, 11, 15, 17, 19, 21, 23, or 25 modulo 26.

**How do you find the modular inverse of a function?**

A naive method of finding a modular inverse for A (mod C) is: step 1. Calculate A * B mod C for B values 0 through C-1 step 2. The modular inverse of A mod C is the B value that makes A * B mod C = 1 Note that the term B mod C can only have an integer value 0 through C-1, so testing larger values for B is redundant. Step 1.

## How do you find the inverse of a number mod 11?

To find the inverse of a number a (mod 11) must find a number n such that a n ≡ 1 (mod 11), or equivalently a pair of numbers such that a n + 11 m = 1. So use the Euclidean algorithm to find these numbers.

### What is the modulo inverse of 10 (under 17)?

Input: a = 10, m = 17 Output: 12 Since (10*12) mod 17 = 1, 12 is modulo inverse of 10 (under 17). Recommended: Please solve it on “ PRACTICE ” first, before moving on to the solution.

**What numbers have an inverse of $11$?**

Yes, only numbers which are relatively prime to 11 will have an inverse $\\mod {11}$. Of, course that would be all numbers $\\{1,\\ldots, 10\\}$. To find the inverse of a number $a\\pmod{11}$ must find a number $n$ such that $an\\equiv 1\\pmod{11}$, or equivalently a pair of numbers such that $an+11m=1$.