a1od = SuperDagger[a1o];
a1id = SuperDagger[a1i];

b1id = SuperDagger[b1i];
b1od = SuperDagger[b1o];
a2id = SuperDagger[a2i];

a2od = SuperDagger[a2o];
b2id = SuperDagger[b2i];
b2od = SuperDagger[b2o];
a3id = SuperDagger[a3i];
a3od = SuperDagger[a3o];
Unprotect[Conjugate];
Conjugate /: MakeBoxes[Conjugate[x_], StandardForm] := TemplateBox[{Parenthesize[x, StandardForm, Power]}, "Conjugate", DisplayFunction -> (SuperscriptBox[#1, "*"] & )]
Protect[Conjugate];



 f = Array[Subscript[U, FromDigits[{##1}]] & , {10, 10}] . (Array[Subscript[np, FromDigits[{##1}]] & , {10}] /. {Subscript[np, 1] -> a1od, Subscript[np, 2] -> b1od,
  Subscript[np, 3] -> a2od, Subscript[np, 4] -> b2od, Subscript[np, 5] -> a3od, Subscript[np, 6] -> a1o, Subscript[np, 7] -> b1o, Subscript[np, 8] -> a2o,
  Subscript[np, 9] -> b2o, Subscript[np, 10] -> a3o});

MatrixForm[Outer[Times, f, Conjugate[f] /. {a1o -> a1od, b1o -> b1od, a2o -> a2od, b2od -> b2o, a3od -> a3o, a1od -> a1o, b1od -> b1o, a2od -> a2o, b2od -> b2o, a3od -> a3o}][[1,1]]]