# 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.