If you have the matrix A, I think it's quite clear that it's skew-symmetric. You only need to verify that .
Let T: R3-->R3, defined by T(x)= a x x
Give the standard matrix A of T, and explain why A is skew-symmetric.
I was able to get the standard matrix of a x x, but i dont really understand how to prove that it is skew symmetric. I can see it in this case, but in general I don't see a rule for it.
I was just under the assumption that I needed to prove it for any A. I showed that for the case of the matrix I had. In class he started talking about proving it in general when I don't have the matrix A. That's where I'm getting stuck, is for all other possible matrices of cross products. Will they all be the same?