MN = 
      Inverse[{{1, -p, 0, 0}, {-(1 - p), 1, -p, 
            0}, {0, -(1 - p), 1, -p}, {0, 0, -(1 - p), 
            1}}]

MR = {{1 - p, 0}, {0, 0}, {0, 0}, {0, p}};

MN /. {p -> 0.3} // MatrixForm

MN /. {p -> 0.7} // MatrixForm

Apply[Plus, MN[[1]] /. {p -> 0.3}]

Apply[Plus, MN[[1]] /. {p -> 0.7}]

MN  .  MR  /. {p -> 0.3} // MatrixForm

MN  .  MR  /. {p -> 0.7} // MatrixForm