P = (1/40)*matrix(c( 0, 20,  5,  5,  5,  5,
                      8,  0,  8,  8,  8,  8,
                     10,  0,  0, 10, 10, 10,
                     10,  0, 10,  0, 10, 10,
                     10,  0, 10, 10,  0, 10,
                     10,  0, 10, 10, 10,  0), nrow=6, byrow=T)
 P
 ##      [,1] [,2]  [,3]  [,4]  [,5]  [,6]
 ## [1,] 0.00  0.5 0.125 0.125 0.125 0.125
 ## [2,] 0.20  0.0 0.200 0.200 0.200 0.200
 ## [3,] 0.25  0.0 0.000 0.250 0.250 0.250
 ## [4,] 0.25  0.0 0.250 0.000 0.250 0.250
 ## [5,] 0.25  0.0 0.250 0.250 0.000 0.250
 ## [6,] 0.25  0.0 0.250 0.250 0.250 0.000

  g = eigen(t(P))$vectors[,1]     # t=transpose for row (not column) eigenvector
  lim.dist = g/sum(g)             # to make vector sum to 1
  lim.dist = as.numeric(lim.dist) # kill complex number notation

g
 ## [1] -0.4719292+0i -0.2359646+0i -0.4247363+0i -0.4247363+0i
 ## [5] -0.4247363+0i -0.4247363+0i

 lim.dist
 ## 0.19607843 0.09803922 0.17647059 0.17647059 0.17647059 0.17647059

lim.dist %*% P   # '%*%' denotes matrix multiplication in R
 ##      [,1]       [,2]      [,3]      [,4]      [,5]      [,6]
 ## 0.1960784 0.09803922 0.1764706 0.1764706 0.1764706 0.1764706