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I am working on the following problem:

If a matrix is antisymmetric (thus A^T = -A), show that

P = {A [tex]\in[/tex] R | A is antisymmetric} is a subset of Rnxn. Also, find the dimension of P.

So far, I've proven that P is a subset of R and I am guessing that, in order for me to find the dimension, I need to find the basis of P first. Here is where I am kind of stuck.

I understand what the properties of the base would be (1. the vectors inside the set will be linearly independent and 2. the basis will be a spanning set for P), but how exactly should I start working so that I can find the basis itself...

A hint would be highly appreciated!

Thanks a bunch guys!