# Prove a variant of Tensor Product

If $A_{1}$, $A_{2}$, $B_{1}$, $B_{2}$ are matrices for which the matrix products $A_{1}A_{2}$ and $B_{1}B_{2}$ are defined, the following rule holds:

$(A_{1} \otimes B_{1})(A_{2}\otimes B_{2}) = (A_{1}A_{2})\otimes(B_{1}B_{2})$

Prove this. Explain that this result makes clear why the transposition in the definition of the Kronecker product is 'necessary'.

Thanks for the help already!

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What did you try so far? It is easier for people to give you good answers if they know what you have been trying. It also shows effort on your part, which often leads to people willing to spend more time answering your question. –  Daan Michiels Feb 11 '13 at 19:16
We just started the topic vector differentiation this week. We use a new reader which explains everything very bad and too abstract. Ive been trying this exercise with some classmates but we had absolutely no idea how solve it. –  Sjoerd Smaal Feb 11 '13 at 19:19
Maybe start by trying a few examples in small dimension. –  Daan Michiels Feb 11 '13 at 19:28