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Combinatorics

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Moderate

Operations that preserve a latin square

COMBIN-0E7XWK

Suppose $L$ is an $n\times n$ latin square. For which of the following operation(s) is the resulting matrix also a latin square?

A

Swap the elements 1 and 2 everywhere they occur.

B

Replace $L$ by its transpose.

C

Replace each element $i$ with $i^2 mod n$

D

Reverse the elements of the first row.