  In this paper we prove an Ax-Schanuel type result for the exponential
functions for general linear groups over $\mathbb{C}$. We prove the result
first for the group of upper triangular matrices and then for the group $GL_n$
of all $n\times n$ invertible matrices over $\mathbb{C}$. We also obtain
Ax-Lindemann type results for these maps as a corollary, characterizing the
bi-algebraic subsets of these maps.
