Table of Contents

## What is meant by multiplicative inverse modulo?

Definition. A modular multiplicative inverse of an integer a is an integer x such that a⋅x is congruent to 1 modular some modulus m. To write it in a formal way: we want to find an integer x so that. a⋅x≡1modm. We will also denote x simply with a−1.

## Can modular multiplicative inverse be negative?

Modular multiplicative inverse function doesn’t work for negative numbers.

**What is the multiplicative inverse of 3 modulo 11?**

4

The multiplicative inverse of “a modulo m” exists if and only if a and m are relatively prime (i.e., if gcd(a, m) = 1). Examples: Input: a = 3, m = 11 Output: 4 Since (4*3) mod 11 = 1, 4 is modulo inverse of 3(under 11).

**What is the inverse of 7 mod 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 9 10?

-10/9

The multiplicative inverse of -9/10 is -10/9. To verify the answer, we will multiply -9/10 with its multiplicative inverse and check if the product is 1.

### What is meant by modular inverse of a number?

The modular inverse of A (mod C) is A^-1

**How do you get the multiplicative inverse?**

Iterate from 0 to M-1,call it i

**What is a modular inverse?**

Modular inverse. The inverse of a number modulo is a number such that . It exists (and is unique if exists) if and only and are relatively prime (that is, ). In particular, if is a prime, every non-zero element of has an inverse (thus making it an algebraic structure known as field).

#### Is the answer for multiplicative inverse properties always 1?

Multiplying a number by its reciprocal (the “multiplicative inverse”) is always one. But not when the number is 0 because 1/0 is undefined!