This was a homework problem that my TA graded but I don't understand why he marked it incorrect. Here is my problem and work:
$V=S_{3}$(symmetric 3x3 matrix ) and $W = s_{3}^{\prime}$ (skew symmetric 3x3 matrix)
I determined the dim of $V = 6 * \frac{3(3+1)}{2}$ However, the dim of W is 3. So, i said since dim V does not equal to dim W then they are not isomorphic