Question: What is the largest k such that if you can multiply 3 3 matrices using k multiplications (not assuming commutativity of multiplication), then you

What is the largest k such that if you can multiply 3 × 3 matrices using k multiplications (not assuming commutativity of multiplication), then you can multiply n × n matrices in time o(n^{lg 7})? What would the running time of this algorithm be?

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