myObject[,,1] # returns a square matrix
myObject[,,2] # returns a square matrix of the same size
...

matrixSum <- myObject[,,1] + myObject[,,2] + myObject[,,3]

matrixSum <- apply(myObject, c(1,2), sum)

myObject <- array(c(1,2,3),dim = c(3,4,3))
myObject
, , 1

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

, , 2

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

, , 3

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

apply(myObject, c(1,2), sum)
     [,1] [,2] [,3] [,4]
[1,]    3    3    3    3
[2,]    6    6    6    6
[3,]    9    9    9    9

rowSums(myObject, dims = 2)
     [,1] [,2] [,3] [,4]
[1,]    3    3    3    3
[2,]    6    6    6    6
[3,]    9    9    9    9