Ehm, the question is rather strange: as a matter of fact, what is called a determinant is interesting because of its properties, which is what you may call the

Ehm, the question is rather strange: as a matter of fact, what is called a determinant is interesting because of its properties, which is what you may call the 'definition'. A bit of a circular argument but: the 'determinant' property is interesting, so it is given a name. The 'property' can be one of many. The most 'obvious' being that the only 'coherent' way to define 'area', 'volume', etc... so that it behaves 'linearly' [i.e. correctly for parallelepipeds] ends up being quite 'complicated' but quite useful at the same time and it receives a name. As it happens, it turns out to be quite useful for theoretically solving linear equations as well (although NOT for real-world solving them). So... It is not weird, it is what it is because it happens to be that way and then it receives a name. There are much weirder things you can do with a matrix which do not have a specific name. Determinants have because they are useful.