Question

The set of integers {0,1,2,3,4,5} under addition modulo 6 forms the so-called group Z₆​. Determine the multiplication table of Z₆​.

Answer 1

The multiplication table of Z₆ is created by multiplying elements {0,1,2,3,4,5} and taking the result modulo 6, resulting in a table that shows how elements combine under this operation.

Step-by-step explanation:

The student has asked to determine the multiplication table of Z₆, which is the set of integers {0,1,2,3,4,5} under addition modulo 6. The operation in this context is multiplication modulo 6, which means that when two numbers are multiplied, the result is taken modulo 6.

Multiplication Table of Z₆

• 0 times any number is 0.
• 1 times any number is that number (identity element).
• Multiplying two numbers and then applying modulo 6 gives the result.

Here is the complete multiplication table for Z₆:

* 0 1 2 3 4 5

0 0 0 0 0 0 0

1 0 1 2 3 4 5

2 0 2 4 0 2 4

3 0 3 0 3 0 3

4 0 4 2 0 4 2

5 0 5 4 3 2 1