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In NSpire the elements of a matrix must be scalars. This implies two things: 1) `[i, j, k, l]` must be written `augment(i,augment(j,augment(k,l)))` 2) the output of det is a scalar The last is the most troublesome for you.

It basically means you need to write your own version of det if you want to use your approach. Now the second part of the question is how to implement this for arbitrary dimensions. The sad part is that the 'programming language' in NSpire is very limited. The first complication is that augment doesn't handle an arbitrary number of arguments. Instead you will need to write a augment_from_list(vectors) which takes one argument (a list of vectors) and augments them. And that is just for augment -- you will need similar helpers in order extend the builtin functions to handle an arbitrary number of arguments.