A Matrix Problem

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:

View the solution

A Matrix Problem Solution

The answer is zero. From the initial information, we can determine that -B = -A, so A and B are equal. Furthermore, we can determine that -C and B - D are equal. Thus, the determinant is equivalent to the top row of A and A, and the bottom row of C and C, so the determinant is zero.

Solution submitted by: MrT

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