Let $K$ be a field, $n \in N$ and d: $M_{n,n}(K) \to K $ an homogeneous and skew invariant transformation where $M_{n,n}(K)$ are the matrices over the field.
Show that there's a $d$ with $d = c * det$, with $c \in K$ and $det$ being the determinant.
Thanks in advance for any help! I've recently really started to like the determinant and it's practical uses and applications, but I yet struggle to fully understand all of them.