I was posed with the question to prove that:
Every square matrix can be written as the sum of 2018 invertible matrices.
My attempt. Since 2018 seemed like a weird number to begin with, my guess was to write the first 2016 with half of them as the identity matrix and other half as $-1$ times the identity matrix so that they cancel out. As for the remaining two matrix I thought I could write one as a symmetric matrix and the other as an skew symmetric matrix. But, now i can see that not every symmetric matrix or skew symmetric matrix is invertible. So, can anyone help me out as to how to proceed?