# #11. Checking Matrix Multiplication

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Prompts for discussion:

Can we extend this method to distinguish between situations when C is “very close” to A \times B vs when C is “far” from A \times B, for a suitable notion of distance between matrices?

Let’s say the Matrix Wizard always outputs I_n and you are always multiplying two permutation matrices. Is it possible to count, in terms of some aspect of the permutation represented by A \times B, the number of vectors \mathbf{x} for which D \mathbf{x} \neq 0?