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 |