Simplify Expressions – Simplify does nothing on a matrix, but works separately for each element

I do some operations that arrive in a matrix

mat = {{- (γ ^ (3/2) / (- γ + Sqrt[1 + γ^2])) + Sqrt[
   1 + γ^2]/ (- γ + sqrt[1 + γ^2]) +
sqrt[γ] (- (
sqrt[γ]/ (- γ + sqrt[
        1 + γ^2])) + γ / (- γ + Sqrt[
       1 + γ^2])),
sqrt[1 + γ^2] (- (
sqrt[γ]/ (- γ + sqrt[
        1 + γ^2])) + γ / (- γ + Sqrt[
       1 + γ^2])) +
sqrt[γ] (- (γ ^ (
3/2) / (- γ + Sqrt[1 + γ^2])) + Sqrt[
      1 + γ^2]/ (- γ + sqrt[1 + γ^2])),
0}, {0, - (γ / (- γ + Sqrt[1 + γ^2])) + Sqrt[
   1 + γ^2]/ (- γ + sqrt[1 + γ^2]), 0}, {0, 0, 1}}

Simplify[] This is nothing (it spits the same again).

But if I copy each element and do Simplify[] For each element separately it simplifies correctly up to 

    {{1, γ, 0}, {0,1,0}, {0,0,1}}

What gives?

TO EDIT:

I just discovered that when I do Simplify[mat[[1]]], makes it really easier to lower. No idea why that works.