# Simplify a Determinant Identity

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## Background

Suppose that $A$ and $B$ are singular and nonsingular matrices respectively. Simplify $\det((A+B)^2−(A−B)^2)$.

## Problem

A wrong solution with a vote of -2 is chosen by Daniel. Why can this happen?

## Possible explanation

That’s because he’s correctly done the expansion until $\det(2AB + 2BA)$.

## Raison d’être of this post

Having spent time on typing a comment, I worry that it will automatically disappear in sooner or later if the accepted answer is deleted. Therefore, I back it up here.

Consider $% $ % However, if $A = 0$ and $B = I_3$, then the answer is clearly zero. As a result, we can’t decude further from $\det(2(AB + BA))$.

## Lessons learnt

The generation of a random matrix/array of integers using randi([imin, imax], m, n). For more details, you may read GNU Octave’s manual.