A student discovers a way to multiply 2×2 matrices using exactly 5 multiplications, instead of Strassen’s 7. What is the number M(n) of multiplications for the resulting algorithm to multiply n×n matrices? Use Θ-notation to express your estimate.
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Students don't discover such things, nowadays. They ask at MSE how to multiply matrices (with all steps). Much as you do concerning $M(n)$, without any own effort. – Sep 27 '17 at 19:29