I am currently experiencing an issue with the output display order in the Wolfram Language and was hoping that you could shed some light on this matter.

When running computations in my script, I have noticed that the output order does not always align with the sequence the commands were written. Specifically, the return from a TeXForm command seems to be consistently appearing after all the other outputs, despite its placement in the sequence of the code.

Here is a snippet of my code for reference:

In[64]:= Array[Subscript[a, #] &, 4, 0] . Array[PauliMatrix, 4, 0]

(*
The error of dot product between two matrices.
https://community.wolfram.com/groups/-/m/t/3090306
The array Array[PauliMatrix,4,0] has three levels,the first of length \
4 and the last with length 2. The array Array[a,4,0] has length 4. \
You can multiply them only in one direction,not in the other.To do \
what you have in mind,you need a generalization of Dot,with the \
instruction to use only the first level of the Pauli array:
*)

Inner[Times, Array[PauliMatrix, 4, 0], 
 Array[Subscript[a, #] &, 4, 0], Plus, 1]

TeXForm[{{Subscript[a, 0] + Subscript[a, 3], 
   Subscript[a, 1] - I Subscript[a, 2]}, {Subscript[a, 1] + 
    I Subscript[a, 2], Subscript[a, 0] - Subscript[a, 3]}}]

Array[Inactive[PauliMatrix], 4, 0] . 
  Array[Subscript[a, #] &, 4, 0] // Activate

prodForCalculation = 
  Inner[Times, Array[PauliMatrix, 4, 0], Array[a, 4, 0], Plus, 1];
forDisplay = a[i_] :> Subscript[a, i];
prodForDisplay = prodForCalculation /. forDisplay

X = {{Subscript[a, 0] + Subscript[a, 3], 
   Subscript[a, 1] - I Subscript[a, 2]}, {Subscript[a, 1] + 
    I Subscript[a, 2], Subscript[a, 0] - Subscript[a, 3]}}

X // Tr

X // MatrixForm

Table[PauliMatrix[i] . X // Tr, {i, 3}] // Simplify

{{1/2, 0, 0, 1/2}, {0, 1/2, 1/2, 0}, 
   1/I {0, -1/2, 1/2, 0}, {1/2, 0, 0, -1/2} } . (X // 
    Flatten) // Simplify

(*
Deriving a Matrix from a Given Matrix Equation.
https://community.wolfram.com/groups/-/m/t/3090848
*)
X = {{Subscript[a, 0] + Subscript[a, 3], 
    Subscript[a, 1] - I Subscript[a, 2]}, {Subscript[a, 1] + 
     I Subscript[a, 2], Subscript[a, 0] - Subscript[a, 3]}};
coeffs = {Subscript[a, 0], Subscript[a, 1], Subscript[a, 2], 
   Subscript[a, 3]};
matrixA = Array[b, {4, 4}];
matrixXgeneric = Array[x, {2, 2}];
solA = Solve[
   Eliminate[{matrixA . (X // Flatten) == coeffs, 
     X == matrixXgeneric}, coeffs], Flatten[matrixA]];
matrixSol = matrixA /. solA[[1]] /. b[__] :> 1;
matrixSol . (matrixXgeneric // Flatten) == coeffs /. 
  Thread[Flatten[matrixXgeneric] -> Flatten[X]] // Simplify
matrixSol . (matrixXgeneric // Flatten) == coeffs // Simplify

(*It does not seem to be a coincidence.There are infinitely many \
matrices A that solve your problem,but they all give the same \
relation between X and the a_i:*)
Simplify[(matrixA /. solA[[1]]) . (matrixXgeneric // Flatten)]
Out[64]= {{Subscript[a, 0] + Subscript[a, 3], 
  Subscript[a, 1] - I Subscript[a, 2]}, {Subscript[a, 1] + 
   I Subscript[a, 2], Subscript[a, 0] - Subscript[a, 3]}}
Out[65]= {{Subscript[a, 0] + Subscript[a, 3], 
  Subscript[a, 1] - I Subscript[a, 2]}, {Subscript[a, 1] + 
   I Subscript[a, 2], Subscript[a, 0] - Subscript[a, 3]}}
Out[67]= {{Subscript[a, 0] + Subscript[a, 3], 
  Subscript[a, 1] - I Subscript[a, 2]}, {Subscript[a, 1] + 
   I Subscript[a, 2], Subscript[a, 0] - Subscript[a, 3]}}
Out[70]= {{Subscript[a, 0] + Subscript[a, 3], 
  Subscript[a, 1] - I Subscript[a, 2]}, {Subscript[a, 1] + 
   I Subscript[a, 2], Subscript[a, 0] - Subscript[a, 3]}}
Out[71]= {{Subscript[a, 0] + Subscript[a, 3], 
  Subscript[a, 1] - I Subscript[a, 2]}, {Subscript[a, 1] + 
   I Subscript[a, 2], Subscript[a, 0] - Subscript[a, 3]}}
Out[72]= 2 Subscript[a, 0]
Out[73]//MatrixForm= \!\(
TagBox[
RowBox[{"(", "", GridBox[{
{
RowBox[{
SubscriptBox["a", "0"], "+", 
SubscriptBox["a", "3"]}], 
RowBox[{
SubscriptBox["a", "1"], "-", 
RowBox[{"I", " ", 
SubscriptBox["a", "2"]}]}]},
{
RowBox[{
SubscriptBox["a", "1"], "+", 
RowBox[{"I", " ", 
SubscriptBox["a", "2"]}]}], 
RowBox[{
SubscriptBox["a", "0"], "-", 
SubscriptBox["a", "3"]}]}
},
GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]}, 
Offset[0.27999999999999997`]}, "Rows" -> {
Offset[0.2], {
Offset[0.4]}, 
Offset[0.2]}}], "", ")"}],
Function[BoxForm`e$, 
MatrixForm[BoxForm`e$]]]\)
Out[74]= {2 Subscript[a, 1], 2 Subscript[a, 2], 2 Subscript[a, 3]}
Out[75]= {Subscript[a, 0], Subscript[a, 1], Subscript[a, 2], Subscript[a, 3]}
During evaluation of In[64]:= Solve::svars: Equations may not give solutions for all "solve" variables.
Out[82]= True
Out[83]= {1/2 (x[1, 1] + x[2, 2]), 1/2 (x[1, 2] + x[2, 1]), 
  1/2 I (x[1, 2] - x[2, 1]), 1/2 (x[1, 1] - x[2, 2])} == {Subscript[a,
   0], Subscript[a, 1], Subscript[a, 2], Subscript[a, 3]}
Out[84]= {1/2 (x[1, 1] + x[2, 2]), 1/2 (x[1, 2] + x[2, 1]), 
 1/2 I (x[1, 2] - x[2, 1]), 1/2 (x[1, 1] - x[2, 2])}
\left(
\begin{array}{cc}
 a_0+a_3 & a_1-i a_2 \\
 a_1+i a_2 & a_0-a_3 \\
\end{array}
\right)

The output generated by this part of the script appears at the end, contrary to my expectations based on its place in the code execution sequence.

From my understanding of the Wolfram Language, I would anticipate the output order aligns with their sequential order in the script. However, my experience seems to be contradicting this understanding.

Could you please provide some insights on why the output may not be displaying in the expected sequence and whether there are any potential solutions I could apply to address this issue?

I would greatly appreciate if you could also point me towards any resources or documentation that might help me understand this aspect of behavior in the Wolfram Language.

Thank you very much in advance for your time and assistance.

Best Regards, Zhao