Exercises\ 6.1.2 If

L

is a latin square of order

n

and

\\\\alpha

is any permutation on

{1,2,3,dots,n}

, denote by

L\\\\alpha

the latin square obtained from

L

by replacing each symbol

x

in

L

by

x\\\\alpha

. Prove that if

L_(1)

and

L_(2)

are orthogonal and

\\\\alpha

and

\\\\beta

are any two permutations, then

L_(1)\\\\alpha

and

L_(2)\\\\beta

are also orthogonal.

Exercises 6.1.2 If L is a latin square of order n and is any permutation on {1,2,3,,n}, denote by L the latin square obtained from L by replacing each symbol x in L by x. Prove that if L1 and L2 are orthogonal and and are any two permutations, then L1 and L2 are also orthogonal