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I try to use @which but it leads me to a page on GitHub with the code, however I want to know the explicit path in my computer i.e. the file that is used when I call the function. for example broadcast(+, A, A) where A is an Array, I thought the path was:

C:UsersuserAppDataLocalJulia-0.6.3sharejuliabasebroadcast.jl

but when I edited it, changing some value return, and then use the function, there is not any change, Which makes me think that it is not the desired file.

This is an attempt to (sort of) summarize what has been written in the comments already.

Before anything, as @daycaster mentioned correctly, changes to Base source files won't take effect until you recompile your system image. So, the path you gave is actually correct.

In the REPL, using @which will tell you where the function is defined (name of the Base file and line number):

julia> @which 3+3
+(x::T, y::T) where T<:UnionInt128, Int16, Int32, Int64, Int8, UInt128, UInt16, UInt32, UInt64, UInt8 in Base at int.jl:53

Integer addition is defined in line 53 of int.jl in the base folder of your local julia installation. In Jupyter (maybe also in Juno?) this is automatically made clickable and will bring you to the respective line on github.

If you told Julia what you favorite editor is, by setting JULIA_EDITOR to e.g. vim, you can use @edit 3+3 to get an editor instance at the right file and line locally.

(Note that there is a URL bug on Windows which leads to incorrect URLs for methods living in standard libraries.)

In any case, as @BogumiłKamiński mentioned, you probably shouldn't modify the julia source in the first place. Just "overwrite" the relevant method in an open Julia session (you can do it in your startup.jl if you want this to be locally permanent):

julia> inv(3)
0.3333333333333333

julia> Base.inv(x::Integer) = begin println("JUHU!"); float(one(x)) / float(x) end

julia> inv(3)
JUHU!
0.3333333333333333

If (for some mysterious reasons) you really want to make the change in a Base source file, you can use Revise.jl, as mentioned by @Gnimuc. This would look like this:

julia> using Revise

julia> Revise.track(Base)

julia> inv(3)
0.3333333333333333

julia> @edit inv(3) # make a change

julia> inv(3)
JUHU!
0.3333333333333333

However, this isn't much different from just overwriting the method yourself. It also won't be permanent.

UPDATE:
I just realized that you're still on 0.6. In that case the file isn't called startup.jl but juliarc.jl. Also the Windows URL bug doesn't effect you then.