Latin Square - Reduced Form

Reduced Form

A Latin square is said to be reduced (also, normalized or in standard form) if both its first row and its first column are in their natural order. For example, the above Latin square is not reduced because its first column is A, C, B rather than A, B, C.

We can make any Latin square reduced by permuting (reordering) the rows and columns. Here switching the above matrix's second and third rows yields

which is reduced: Both its first row and its first column are alphabetically ordered A, B, C.