A = matrix(c(0.5, 0.5,   0,
             0.5,   0, 0.5,
               0, 0.5, 0.5), nrow = 3, byrow=T)
A
     [,1] [,2] [,3]
[1,]  0.5  0.5  0.0
[2,]  0.5  0.0  0.5
[3,]  0.0  0.5  0.5

A2 = A %*% A;  A2
     [,1] [,2] [,3]
[1,] 0.50 0.25 0.25
[2,] 0.25 0.50 0.25
[3,] 0.25 0.25 0.50

g = eigen(t(A))
sg = as.numeric(g$vec[,1])
  # 1st col of vector output is vector you want
  # 'as.numeric' gets rid of complex-nr notation
sg = sg/sum(sg)  # scale so elements add to 1
sg
[1] 0.3333333 0.3333333 0.3333333
g %*% A  # check
          [,1]      [,2]      [,3]
[1,] 0.3333333 0.3333333 0.3333333