Every nxn matrix can be written as a linear combination of matrices in GL(n,F)

[fishshoe]

Homework Statement

Prove: Every nxn matrix can be written as a linear combination of matrices in GL(n,F).

Homework Equations

GL(n,F) = the set of all nxn invertible matrices over the field F together with the operation of matrix multiplication.

The Attempt at a Solution

I know all matrices in GL(n,F) are invertible and hence have linearly independent columns and rows. I was thinking perhaps there is something about the joint bases for the n-dimensional column and row spaces, respectively, that could provide a basis for M_{nxn}(F), which has dimension of n^2. But I'm not really sure if that works.

 

[fishshoe]

Okay, I figured it out. Nevermind (although once a post gets buried two screens back, it's not likely to be answered anyway, even if it has zero replies...).