page 6 - Defn 1.6

Definition 1.6 A set of t latin squares are mutually orthogonal if each pair of latin squares is orthogonal.

Denote the two latin squares of order 3 from Eg 1.1 by A₁,A₂.
Is it possible to find a third latin square A₃ of order three such that
A₁,A₂,A₃ are mutually orthogonal latin squares?

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