creating a matrix with a nested for loop

This is a practice question to prep for an exam. I'm given the following code:

     W=matrix(1:16,byrow=T,ncol=4)
print(W)

fmat=function(W){
n=nrow(W)

      for (i in 1:n){
      for (j in 1:n){
        W[j,i]=W[i,j]+W[j,i]
      }
      }

      return(W)
}

print(fmat(W))

We have to "run" the code on paper and then check our answers by running the code in R. I wrote out the correct matrix for W but I got fmat(W) wrong. R gives me the following output for fmat(W):

     [,1] [,2] [,3] [,4]
[1,]    2    9   15   21
[2,]    7   12   24   30
[3,]   12   17   22   39
[4,]   17   22   27   32

where I had written down that fmat(W) would equal:

     [,1] [,2] [,3] [,4]
[1,]    2    7   12   17
[2,]    7   12   17   22
[3,]   12   17   22   27
[4,]   17   22   27   32

What exactly is going on here? I had interpreted the function to calculate that, for example, w[2,1]=w[1,2]+w[2,1], which is 2+5=7.