Why did matrix, pmatrix, and cases stop working when I added the amsmath package?

If you used the plain.tex versions of matrix, pmatrix, or cases in a document and then later converted the document to use the amsmath package (or one of the AMS documentclasses, which automatically call the amsmath package internally), the instances of those commands will produce error messages. The problem is that when was originally created, it adopted most of its mathematics features straight from plain.tex. But in the case of matrix, pmatrix, cases this was a mistake—the plain.tex syntax for them is decidedly non- in style, for example the fact that they use cr instead of
to mark line breaks, and they don't use begin and end. In basic this mistake will be perpetuated at least until 3 appears, in order to avoid breaking existing documents. But no existing documents that were written with the amsmath package have that syntactic problem, as amsmath provides proper -syntax versions of matrix and the others. The possibility of optionally allowing the plain.tex variants to make document conversion easier seems ill-advised since those variants are so blatantly wrong in a context.