I want to subscript with characters to make output of a matrix, and followings can be done

Subscript[a, bb] // TraditionalForm
Subscript[a, b,b] // TraditionalForm
Subscript[Subscript[a, b], b] // TraditionalForm

The results are following $$ a_{bb}\\ a_{b,b}\\ a_{b_b} $$ I want the first format.

But, I need to subscript $a$ with elements inside a list, so,

list = {b,c,d};
Subscript[a, list[[1]] list[[1]]] // TraditionalForm
Subscript[a, list[[1]], list[[1]]] // TraditionalForm
Subscript[Subscript[a, list[[1]]], list[[1]]] // TraditionalForm

Then, the result is $$ a_{b^2}\\ a_{b,b}\\ a_{b_b} $$

I don't want the second or the third. So, How do I prevent that $b^2$? Or, how do I erase comma from second code?

I want to use Subscripts to prettify a matrix and started the following way

Subscript[a, bb] // TraditionalForm
Subscript[a, b,b] // TraditionalForm
Subscript[Subscript[a, b], b] // TraditionalForm

The results are $$ a_{bb}\\ a_{b,b}\\ a_{b_b} $$ I want to use the first type.

But, I need to create the Subscript $a$ with elements from a list, like so

list = {b,c,d};
Subscript[a, list[[1]] list[[1]]] // TraditionalForm
Subscript[a, list[[1]], list[[1]]] // TraditionalForm
Subscript[Subscript[a, list[[1]]], list[[1]]] // TraditionalForm

Then, the result is $$ a_{b^2}\\ a_{b,b}\\ a_{b_b} $$

Sticking with the first type; So, How do I prevent that $b^2$? Or, how do I erase the comma from second output?