Greets, I'm a bit confused about the definition of cosets as of now, here's my problem:

I'll represent a 3x3 matrix using the first integer for row number and the second for column number. Thus 11 = 1 means there's a 1 in the upper left corner of the matrix, 12 is a step to the right from 11 and 21 is a step down.

Given the group G of 3x3 matrices under multiplication with the following properties:

11 = 1, 12 = a, 13 = b

21 = 0, 22 = 1, 23 = c

31 = 0, 32 = 0, 33 = 1

Where a,b,c are members of Z[n], n positive integer

We have the following subgroup H:

11 = 1, 12 = d, 13 = e

21 = 0, 22 = 1, 23 = -d

31 = 0, 32 = 0, 33 = 1

Where d,e are members of Z[n]

What are the left cosets of H in G?

Any advice/clarification on how to compute this would be great.

Thanks in advance.