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Two dimensional matrix-like data type using lists and/or mutable lists

I am trying to think of an implementation of a two dimensional matrix-like data type.
Normally I would take an array of arrays but I’m bound to a relatively low language level which only provides lists and mutable lists, because this is part of (but not an exercise itself, I could simply use an inefficient solution) a software project at university. In this, we are only allowed to use a specific language level.
So of cause I could take a list of mutable lists and, in search of an item in row n and column m, get the m-th mutable list and go throught it until position n. But isn’t there a better solution than going through the whole list?

Scheme’s define in Common Lisp

In Common Lisp, we have to use the let form to declare a new lexically-scoped variable. This means that the code either looks like that written in C89 (all variables declared on top of scope), or acquires unreadably deep nesting. let* is somewhat useful, but is not always applicable.