Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Here is a really basic example. Suppose that $\phi:M_n(K)\rightarrow K$ satisfies $(a)$$\phi$ is multilinear,
$(b)$$\phi$ is alternating and $(c)$$\phi(E_n)=1$. Then it follows $(d))$$\phi(A)=\det (A)$.
