Vector space/Tensor product/Multiplicative properties/Fact

Let ${}K$ be a field, and let ${}U,V,W$ denote ${}K$-vector spaces. Then the following statements hold. (in the sense of a canonical isomorphy).

1. We have

   ${}U\otimes _{K}V\cong V\otimes _{K}U\,.$

2. We have

   ${}U\otimes _{K}{\left(V\otimes _{K}W\right)}\cong {\left(U\otimes _{K}V\right)}\otimes _{K}W\,.$

Write a proof