L={{1,0,0},{0.5,1,0},{0.5,0.69,1}};
U={{2,-1,2},{0,6.5,-2},{0,0,1.38}};
L.U//MatrixForm

A={{1,4,1},{1,6,-1},{2,-1,2}};
P={{0,0,1},{0,1,0},{1,0,0}};
P.A//MatrixForm