Simplify doesn’t do anything on a matrix, but works fine on its elements separately

I am performing some operations which arrive at 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}} 

Performing Simplify[] on this does nothing (it spits the same thing back out).

However, if I copy each element and perform Simplify[] on each element separately, it correctly simplifies down to

 {{1,γ,0},{0,1,0},{0,0,1}} 

What gives?

EDIT:

I just discovered that if I do Simplify[mat[[1]]], it properly simplifies down. No idea why that works.