The tensor product has the following properties. Note that all vector spaces are over the same field . (Associativity) There exists an isomorphism
$\tau: (V_{1}\otimes....\otimes V_{n})\otimes(W_{1}\otimes....\otimes W_{m}) \to V_{1}\otimes...\otimes V_{n}\otimes W_{m} \otimes....\otimes W_{m}$
for which $\tau[((v_{1}\otimes....\otimes v_{n})\otimes(w_{1}\otimes....\otimes w_{m}))]= v_{1}\otimes...\otimes v_{n}\otimes w_{m} \otimes....\otimes w_{m}$
some idea? i don't know how to start. The other properties are commutativity and the existence of an isomorphism but first i want to see how to prove this isomorphism for associativity and get an idea to continue with the next properties