page 5 - Lemma 1.5 and Qu 1.3

Lemma 1.5

1. Let A be a latin square of order n.
   Let α be a permutation on {1,…,n} (i.e. α is a bijection of {1,…,n}).
   Then α(A) is a latin square of order n.
2. Let A,B be two orthogonal latin squares of order n.
   Let α,β be two permutations on {1,…,n}.
   Then α(A),β(B) are two orthogonal latin squares of order n.

Think about how you would prove this lemma
(we will discuss this in the lecture).

Question 1.3.  Explain why this means that we can always write the first row of a latin square of order n as  (1, 2,…,n).

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