Suppose that $A$ and $B$ are singular and nonsingular matrices respectively. Simplify $\det((A+B)^2−(A−B)^2)$.
A wrong solution with a vote of -2 is chosen by Daniel. Why can this happen?
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 $\det(2(AB + BA))$.
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.