(Because---obviously---since the determinant is the product of the eigenvalues,

It's amazing how rarely people -- including textbook authors -- actually bother to point this out. (Admittedly, it's only true over an algebraically closed field such as the complex numbers.) Were you by any chance using Axler?

it serves as a measure of how the transformation distorts area; if the determinant is zero, it means you've lost a dimension in the mapping, so you can't reverse it. But it wouldn't have been "obvious" if I had only read the Wikipedia article.)

While I certainly agree with the main point of your comment, I nevertheless think that this particular comparison illustrates mainly that the mathematical Wikipedia articles still have a way to go. (Indeed, the property of determinants mentioned above is buried in the middle of the "Further Properties" section of the article, whereas I think it ought to be prominently mentioned in the introduction; in Axler it's the definition of the determinant [in the complex case]!)