How to prove this property of the cross product?

Question

Mathematics

Hello, I looked through various books, articles on the Internet and even I can’t find anywhere an understandable (but not from the “it’s obvious” series) proof of the additivity of the vector product:
[a + b, c] = [a, c] + [b, c]

Can someone tell me where to look

Answer 1

This is simply done by definition. You paint the left expression through the determinant and by the properties you get 2 determinants, which are the right side of the equality