Creating a Symbolic Matrix

Question

Probably very simple, but I don't know where to start with this. How do I go about creating a symbolic matrix, such as the one below?

I want to be able to use this so that any list of lists that are entered to signify a matrix can be read as having indices {i,1,m},{j,1,n}, and then I can use another rule using the terms in the matrix, ai,j.

I found an answer that mentioned SymbolicMatrix, but this no longer seems to work on the most up-to-date versions of Mathematica.

EDIT: This seems to be trickier than I first thought. Essentially, whenever I enter a list of lists, such as mat[{{1,2,3},{4,5,6},{7,8,9}], I want to be able to automatically recognise that the first list corresponds to a1,1,a1,2,a1,3, the second list to a2,1,a2,2,a2,3, and the third list (in this example) to a3,1,a3,2,a3,3.

I then aim to write a rule that, when values of I and j are selected, gives back a list of {ai,j+1, ai,j-1, ai-1,j, ai+1,j}.

Answer 1

myMatrix[n_Integer, m_Integer] := 
 Table[Subscript[a, i, j], {i, n}, {j, m}] // MatrixForm

myMatrix[3, 4] 

Answer 2

As mentioned in the comments, it is probably easier to stay away from using subscripts, which are primarily a formatting command. Your task is readily accomplished using Array, and defining a function to extract the elements you want:

mat = Array[a, {4, 5}]
fun[m_, i_, j_] := {a[i, j + 1], a[i, j - 1], a[i - 1, j], a[i + 1, j]};

mat defines the matrix and fun extracts the specified elements. For example:

fun[mat, 3, 4]
{a[3, 5], a[3, 3], a[2, 4], a[4, 4]}