Rcpp matrix: loop over rows, one column at a time

Question

This is my first time trying Rcpp and this very simple problem is giving me trouble. I want to use nested for loops to operate on individual values of a matrix, one column at a time. The script I'm aiming for would look something like this:

src <- '
    Rcpp::NumericMatrix Am(A);
    int nrows = Am.nrow();
    int ncolumns = Am.ncol();
    for (int i = 0; i < ncolumns; i++){
        for (int j = 1; j < nrows; j++){
            Am[j,i] = Am[j,i] + Am[j-1,i];
        }
    }
    return Am;
'
fun <- cxxfunction(signature(A = "numeric"), body = src, plugin="Rcpp")
fun(matrix(1,4,4))

The desired output would be this:

     [,1] [,2] [,3] [,4]
[1,]    1    1    1    1
[2,]    2    2    2    2
[3,]    3    3    3    3
[4,]    4    4    4    4

The problem is obviously in this line, where I don't know how to refer to individual elements of the matrix.

Am[j,i] = Am[j,i] + Am[j-1,i];

Apologies if this is a stupid newbie question. Any hint would be appreciated!