P={{0.1, 0.2, 0.7},{0.2, 0.4, 0.4},{0.1, 0.3, 0.6}};
α={0.2, 0.3, 0.5};
MatrixForm[Table[{n,MatrixForm[MatrixPower[P,n]],MatrixForm[α.MatrixPower[P,n]]},{n,1,4,1}]]
MatrixForm[Table[{n,MatrixForm[MatrixPower[P,n]],MatrixForm[α.MatrixPower[P,n]]},{n,5,100,5}]]