0

Less so wondering what the answer is, but more so wondering how to solve these. I have others I've done, but I kind of just guessed combinations and it worked.

I rather not just sit here guessing different matrices until something works with brute force. Is there some sort of method or thought process that goes into these problems? Or is it just knowing matrices very well and a "you know when you see it" type of thing?

EDIT: $A^2*B^2 \neq (AB)^2$ instead, sorry I forgot the not equals part.

MathMajor
  • 6,478
Carson Wood
  • 193
  • Sorry I typed it in wrong, it's not equals instead of equals. If you didn't see it before the edit. My bad! – Carson Wood Sep 15 '16 at 01:49
  • Are the matrices $2\times 2$? If so, you could compute both of $A^2B^2$ and $(AB)^2$ and then compare entries. – Alex Ortiz Sep 15 '16 at 01:49
  • @KonKan $AB\ne BA$ doesn't generally imply $A(AB)B\ne A(BA)B$ does it? (It does if $A$ and $B$ are invertible of course.) – anon Sep 15 '16 at 02:18

1 Answers1

0

Let $A$ be $$\begin{pmatrix}0 & 1 \\ 0 & 0\end{pmatrix}$$

What is $A^2$? So then what is the left-hand side, regardless of what $B$ is? It isn't so hard to find that matrix $B$ now.

David P
  • 12,320