A={{(1/2),(1/2),0,0},{(1/2),(1/2),0,0},{0,0,(1/2),(1/2)},{0,0,(1/2),(1/2)}};
MatrixPower[A,2]==A

B={{0,1,0,0},{0,0,1,0},{0,0,0,1},{0,0,0,0}};
Table[MatrixPower[B,k]==ConstantArray[0,{4,4}],{k,10}]