Let $R$ be a commutative ring with units. Suppose that $\{A_i \}$ and $\{B_j\}$ are two linearly independent families of $n \times n$ matrices over $R$.

Is it true that the set $\{A_i \otimes B_j \}$ is linearly independent?

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    $\begingroup$ Yes, this follows from basic facts about tensor products. $\endgroup$ – Lord Shark the Unknown Aug 21 '18 at 14:52
  • $\begingroup$ @LordSharktheUnknown Thank you. Do you know where I can find a good reference for this? Perhaps a book or a paper. I am not familiar with Tensor products. Thank you again. $\endgroup$ – NongAm Aug 21 '18 at 15:02
  • $\begingroup$ The best reference would be a nice beginners book on Algebra. Dummit and Foote does nicely for me. $\endgroup$ – астон вілла олоф мэллбэрг Aug 21 '18 at 15:07

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