An Introduction to Mathematical Structure

Here are the answers to the challenges:
 
 
2) Take the numbers 2, 4, 6, 8 and multiply them mod 10 (so just write down the last digit).
x 2 4 6 8
2 4 8 2 6
4 8 6 4 2
6 2 4 6 8
8 6 2 8 4
3) Take the numbers 1, 2, 3, 4 and multiply them mod 5.
x 1 2 3 4
1 1 2 3 4
2 2 4 1 3
3 3 1 4 2
4 4 3 2 1
4) Take the numbers 1, 3, 5, 7 and multiply them mod 8.
x 1 3 5 7
1 1 3 5 7
3 3 1 7 5
5 5 7 1 3
7 7 5 3 1
5) Rotations of a square
  I Q Q² Q³
I I Q Q² Q³
Q Q Q² Q³ I
Q² Q² Q³ I Q
Q³ Q³ I Q Q²
6) Symmetries of a rectangle
  I V H R
I I V H R
V V I R H
H H R I V
R R H V I
7) The T-shirt!
  Same BTF I-O Both
Same Same BTF I-O Both
BTF BTF Same Both I-O
I-O I-O Both Same BTF
Both Both I-O BTF Same