Golang: Why does response.Get("headerkey") not return a value in this code?

This has been bothering me for the past couple hours, I'm trying to get a response header value. Simple stuff. If I curl a request to this running server, I see the header set, with curl's -v flag, but when I try to retrieve the header using Go's response.Header.Get(), it shows a blank string "", with the header's length being 0.

What frustrates me even more, is that the header value is actually set within the response when I print out the body (as demonstrated below).

Any and all help with this is appreciated, thanks in advance.

I have this code here:
http://play.golang.org/p/JaYTfVoDsq

Which contains the following:

package main

import (
	"fmt"
	"io/ioutil"
	"net/http"
	"net/http/httptest"
)

func main() {
	mux := http.NewServeMux()
	server := httptest.NewServer(mux)
	defer server.Close()

	mux.HandleFunc("/", func(w http.ResponseWriter, r *http.Request) {
		r.Header.Set("Authorization", "responseAuthVal")
		fmt.Fprintln(w, r.Header)
	})

	req, _ := http.NewRequest("GET", server.URL, nil)
	res, _:= http.DefaultClient.Do(req)

	headerVal := res.Header.Get("Authorization")
	
	fmt.Printf("auth header=%s, with length=%d\n", headerVal, len(headerVal))
	content, _ := ioutil.ReadAll(res.Body)

	fmt.Printf("res.Body=%s", content)
	res.Body.Close()
}

The output to this running code is:

auth header=, with length=0
res.Body=map[Authorization:[responseAuthVal] User-Agent:[Go-http-client/1.1] Accept-Encoding:[gzip]]

This line:

        r.Header.Set("Authorization", "responseAuthVal")

set the value of r *http.Request, that is the incomming request, while you want to set the value of w http.ResponseWriter, the response that you will receive.

The said line should be

        w.Header().Set("Authorization", "responseAuthVal")

See this playgroud.