# Tensor products and linear transformations

If $E$ and $F$ are linear transformations. How does one prove that $rank(A \otimes B)=rank(A) rank(B)$ where $\otimes$ is the tensor product. This is a question I do not know how to approach. Can I get some help?

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Sorry, I can't quite comment yet. Try to prove (an ostensibly easier thing to do) that if $A:V\to W$ and $B:U\to Z$ (so that $A\otimes B:V\otimes W\to U\otimes Z$ then $\text{im }(A\otimes B)=(\text{im}(A))\otimes(\text{im}(B))$. This should be very clear by definition. and then apply the fact that dimension is multiplicative with respect to tensor products.