What are the elements and order of the subgroup <[4]> in Z13?

[zoner7]

Homework Statement

Assume that the nonzero elements of Z13 form a group G under multiplication [a] = [ab].
a) List the elements of the subgroup <[4]> of G, and state its order

The Attempt at a Solution

So I thought this would be like some of the previous problems.

I assumed that i was simply asked to keep adding 4 and writing down the values until the value reached 0.

The process would follow as such:

[4] [8] [12] [3] [7] [11] [2] [6] [10] [1] [5] [9] [0]

After placing these elements in order, I would say that the subgroup is of order 13.

My intuition is clearly wrong, because the answer in the back of the book reads:

{[1],[3],[4],[9],[10],[12]} o(<[4]>) = 6

How in the world do they get this answer?

 

[Dick]

It says 'multiplicative subgroup'. Don't add 4. Multiply by 4.

 

[zoner7]

well... somebody feels stupid, namely me.

Thanks for the help, buddy.