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?
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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