here is the quastion:
Let n be an odd integer and let A = (aij) be an n × n matrix that satisfies
the condition aij + aji = 0 for all 1 =< (i, j )=< n. Prove that |A| = 0.
i tried every possible way which i know but didnt succeed
otherwise the claim is true and very easy to prove: since we have: because is odd. therefore and hence