In the $2 \times 2$ multiplication square below, the boxes at the end of each row and the foot of each column give the result of multiplying the two numbers in that row or column.

7 | 5 | 35 |

3 | 4 | 12 |

21 | 20 |

The $3 \times3$ multiplication square below works in the same way. The boxes at the end of each row and the foot of each column give the result of multiplying the three numbers in that row or column.

15 | |||

108 | |||

224 | |||

144 | 8 | 315 |

The numbers $1 - 9$ may be used once and once only.

Can you work out the arrangement of the digits in the square so that the given products are correct?