finding a base and dimension of a 3 x 3 matrix that represents all skew-symmetric matrices above the complex field

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I'm suppose to find that matrix, and I was only given the final answer of the dimension which is 3.

But everything I tried so far is leading me to one of the rows being zeroed and therefore the dimension isn't 3.

I know the form of skew-symmetric matrices well, but so far I only dealt with it above the rational numbers, maybe I am missing something.

The matrix have to represent all 3x3 skew symmetric matrices above COMPLEX field.