Question: Please show work and explain Construct two Latin squares A, S of order 5 with entries in Z5 that simultaneously satisfy each of the following

Please show work and explain

Construct two Latin squares A, S of order 5 with entries in Z5 that simultaneously satisfy each of the following properties: (a) A, S are orthogonal. (b) A is orthogonal to its transpose AT. (cl S is svmnietric and idempotent

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