The matrix modes do not change the matrix itself, so identity matrix is identity matrix everywhere.
The matrix modes change which matrix the following commands operate on. That is, whether any subsequent commands work with the projection matrix, or with model*view matrix, or with texture matrices etc.
This might sound a bit confusing, but it's one of OpenGL's design decisions - there's a bunch of commands that operate on some state or object, and only other state settings determine which object exactly they operate on.