'determinant()' noun form for linear algebra ?

I play with low-degree (n < ~6) linear systems all the time, and it makes no sense to constantly spit out all n! terms of the verious determinants that are produced.

Cramer's Rule can often be much more perspicuous than the algebraic form for linear solutions of this type.

I noticed that the 'detout:true' will 'factor out' the denominator determinant when inverting the matrix, but this denominator is still an algebraic expression instead of a determinant representation.

Is there any way to display determinants like matrices, except using "|" brackets instead of "[" and "]" brackets?

After doing some Google searches on "determinant representations", it is probably too much to hope that Maxima can "factor" algebraic expressions back into a determinantal form.