Question

In modular 26 arithmetic, what is the multiplicative inverse of 9?

a) 2
b) 3
c) 4
d) 5

Answer 1

In modular 26 arithmetic, the multiplicative inverse of 9 is 19.

Step-by-step explanation:

In modular 26 arithmetic, the multiplicative inverse of 9 is the number that, when multiplied by 9, gives a result of 1 when taken modulo 26. To find the multiplicative inverse, we can use the Extended Euclidean Algorithm:

1. Step 1: Write down the equation 9x + 26y = 1, where x and y are unknown variables.
2. Step 2: Apply the Extended Euclidean Algorithm to solve for x and y.
3. Step 3: Once you find the values of x and y, take the remainder of x modulo 26 as the multiplicative inverse of 9.

Using the Extended Euclidean Algorithm, we find that x = -7 and y = 2. Taking the remainder of x modulo 26 gives us the multiplicative inverse of 9 as 19. Therefore, the multiplicative inverse of 9 in modular 26 arithmetic is 19.