Find number of skew-symmetric matrices of order $3\times 3$ in which all non-diagonal elements are different

Question

Find number of skew-symmetric matrices of order $3\times 3$ in which all non-diagonal elements are different and belong to the set $\{-9,-8,-7,…,7,8,9\}$

My Attempt:
I did a simple calculation and obtained $$\binom{9}{3}\times(3!)\times 2^3=4032$$

But answer given is $$\frac{4032}{6}=672$$

Why has it been divided by $6$

Answer 1

The given answer would be correct if the problem specified "up to permutations of rows and columns". But it did not, and your answer is correct.