Here is one approach.
set.seed(123)
MAT <- matrix(runif(25), nrow = 5)
MAT
[,1] [,2] [,3] [,4] [,5]
[1,] 0.2875775 0.0455565 0.9568333 0.89982497 0.8895393
[2,] 0.7883051 0.5281055 0.4533342 0.24608773 0.6928034
[3,] 0.4089769 0.8924190 0.6775706 0.04205953 0.6405068
[4,] 0.8830174 0.5514350 0.5726334 0.32792072 0.9942698
[5,] 0.9404673 0.4566147 0.1029247 0.95450365 0.6557058
BINOM <- function(P) rbinom(n = 1, size = 1, prob = P)
apply(X = MAT, MARGIN = c(1,2), BINOM)
[,1] [,2] [,3] [,4] [,5]
[1,] 0 1 1 1 1
[2,] 1 0 1 0 1
[3,] 1 1 1 0 1
[4,] 1 0 1 0 1
[5,] 1 0 0 1 0