Haskell has a very neat interface for this, in that you build a special type which remembers the dimensions of a matrix as you build them, and then return either the result or a failure.

It's very simple to build a function which doesn't have to understand the possible dimension conflicts and lift it to work on this new type, returning an either (or a maybe, if there's only one failure mode) in place of a definite value.

It's also very simple to propagate such errors forward, so they'll short circuit a computation when you have non-matching matrices used in a calculation that's multiple steps.

In Haskell, I don't have to remember to write special functions which guard against this: I write functions that operate on the matrices and add the guarding at the very end. I can ensure that all my calls use the guarding functions, because they have a different type signature.

Trying to do this same thing in Python require that I remember to always use the guarded calls, and doesn't have as clean of an interface to create the guarded functions from standard functions.

What does it matter? No type-system will magically know ahead of time what the contents of the file will be before you run the program, but it can force you to do the appropriate checks when you do read it from the file.