Lately I have been been studying basis and demension. For a more interesting problem I wanted to see if I could find the basis of the vector space of all 3x3 skew symetric matricies. Usually, I can find a general form for these types of problem. Such as the general form of a symetric matricie. But skew symetric matricies seem to have more than one form [0 a b] [-a 0 c] [-b -c 0] and [0 a -b] [-a 0 -c] [b c 0] I proved that this form of a skew symetric matrice is a basis [0 a b] [-a 0 c] [-b -c 0] but is it true for the vector space of all 3x3 skew symetric matricies of that form or all skew symetric matricies?