Sunday, 10 April 2016

linear algebra - Product of invertible matrices

I was posed with the question to prove that every square matrix can be written as the product of 2018 invertible matrices.



Since 2018 seemed like a weird number to begin with, my guess was to first multiply as many identity matrices as needed and then take a product of required number of invertible matrices to get the desired square matrix. How can we prove this is always possible?
Or if there is a fault in my logic can someone point it out.

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