Add all elements in matrix R

Reduce will work

 Reduce(`+`,m)
    [1] 2148

You can do sum. It also has the option na.rm to remove the NA values.

 sum(m)
 #[1] 2148

In general, sum works for vector, matrix and data.frame

Benchmarks

 set.seed(24)
 m1 <- matrix(sample(0:20, 5000*5000, replace=TRUE), ncol=5000)
 system.time(sum(m1))
 #  user  system elapsed 
 # 0.027   0.000   0.026 

 system.time(sum(colSums(m1)))
 # user  system elapsed 
 # 0.027   0.000   0.027 

 system.time(Reduce('+', m1))
 #  user  system elapsed 
 #25.977   0.644  26.673