I think a much more insightful discussion would be to ask, why matrix multiplication is so much more useful than Hadamars product: https://en.wikipedia.org/wiki

I think a much more insightful discussion would be to ask, why matrix multiplication is so much more useful than Hadamars product: https://en.wikipedia.org/wiki/Hadamard_product_(matrices) https://en.wikipedia.org/wiki/Hadamard_product_(matrices) Hadamars product/elementwise multiplication is also commutative.