# Math Help - General Linear Group Proof Help

1. ## General Linear Group Proof Help

Let
A Mn(F).
Prove that A GLn(F) if and only if the columns of A form a basis for Fn.

2. $GL_n(F)$ is the group of invertible n by n matrices on F. The columns of a matrix span the image of the matrix in $F^n$. If those columns form a basis for $F^n$, then the image is the entire space and so the matrix is invertible.