A  =  2*IdentityMatrix[5]

Do[{A[[i, i + 1]] = -1, A[[i + 1, i]] = -1}, {i, 1, 
        4}]

MatrixForm[A]

{LU, P, ConditionNumber}  =  LUDecomposition[A]

Upper[LU_?MatrixQ] := 
      LU Table[
          If[i ≤ j, 1, 0], {i, Length[LU]}, {j, 
            Length[LU]}]

Lower[LU_?MatrixQ] := 
      LU - Upper[LU] + IdentityMatrix[Length[LU]]

MatrixForm[Lower[LU]]

MatrixForm[Upper[LU]]

Lower[LU]*Upper[LU]