Welcome back to the Maine Page! This year, all of our problems are going to involve topics covered in the five annual Maine Association of Math Leagues meets. New problems will be posted every week after the results of the first meet are posted on www.maml.net. Until then, here's a little problem to hold you over:

Suppose that A, B, C, and D are real numbers such that the following matrix equation holds true:
 

Determine the value of the following determinant: