Question: In modular arithmetic, what is the multiplicative inverse of 3 modulo 11?
Options:
4
7
8
9
Correct Answer: 7
Solution:
The multiplicative inverse of 3 mod 11 is 4, since (3 * 4) mod 11 = 12 mod 11 = 1.
In modular arithmetic, what is the multiplicative inverse of 3 modulo 11?
Practice Questions
Q1
In modular arithmetic, what is the multiplicative inverse of 3 modulo 11?
4
7
8
9
Questions & Step-by-Step Solutions
In modular arithmetic, what is the multiplicative inverse of 3 modulo 11?
Step 1: Understand what a multiplicative inverse is. It is a number that, when multiplied by the original number, gives a result of 1 in modular arithmetic.
Step 2: We need to find a number 'x' such that (3 * x) mod 11 = 1.
Step 3: Start testing numbers for 'x' from 1 up to 10 (since we are working modulo 11).
Step 4: Test x = 1: (3 * 1) mod 11 = 3 mod 11 = 3 (not 1).
Step 5: Test x = 2: (3 * 2) mod 11 = 6 mod 11 = 6 (not 1).
Step 6: Test x = 3: (3 * 3) mod 11 = 9 mod 11 = 9 (not 1).
Step 7: Test x = 4: (3 * 4) mod 11 = 12 mod 11 = 1 (this is what we want!).
Step 8: Conclude that the multiplicative inverse of 3 modulo 11 is 4.
Multiplicative Inverse – The multiplicative inverse of a number 'a' modulo 'm' is a number 'b' such that (a * b) mod m = 1.
Modular Arithmetic – A system of arithmetic for integers, where numbers wrap around upon reaching a certain value (the modulus).
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