I was trying to understand what is meant by "area preserving map"?. I was going through the Wolfram article about the area preserving map here but any motivation, intuition or visualization to understand the area-preserving maps, like how it is connected with the determinant being $\pm 1$?, would not it be helpful if we could visualize the area-preserving maps?.
I don't think this soft question about the motivation about the area-preserving maps has been asked before, also will be helpful if one could help with references?. Also, I find it in many research articles.
I could find the following questions on MSE-