I'm really putting some effort into understanding the core idea behind determinants. For a 2x2 matrix, I obviously saw how to derive the formula for the determinant (using AA^-1=I). The question is, how did they define the |A| for higher order matrices? I'm reading a textbook on linear algebra and it uses permutations in its definition of the determinant? What was the motivation for such a definition? How did they know that such a definition can be applied to all nxn matrices???