Counting the number of specific integers per column in an R matrix

I have a matrix (10 x 100) where I need to count the number of each integer per column so I have a final matrix that is (3 x 100). Counts for 0, 1, and 2 per column.

I think the apply function will be useful here, the code I provided is a solution I envision.

Any help will be greatly appreciated.

library(dplyr)
set.seed(100)
a <- matrix(sample(0:2, size=100, replace=TRUE), nrow=10, ncol=100)
out <- apply(a, 2, function(x) count(x))

 Desired output: rows are the sum of each variable "0, 1, 2"

   1 2 3 ...  n
 0 1 1 3
 1 6 3 3
 2 3 6 4