# Thread: idemponent symmetric latin square

1. ## idemponent symmetric latin square

prove there exists an idempotent latin square of order n if and only if n is odd.

i have been working at this for ages. Ive been trying to show that there are n^2 entries since its idempotent n of them are fixed, and then the others have a "partner" because of the symmetric property. but the fact that n needs to be odd is not working for me

2. sorry idempotent symmetric latin square *