# General Linear Group Proof Help

• November 3rd 2009, 09:38 PM
amm345
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.

• November 4th 2009, 01:55 AM
HallsofIvy
$GL_n(F)$ 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.