Question

I need a refresher on matrix multiplication (2x2 times a 2x2).

So I have these two matrices:\[\Large X^{-1}(0)\quad=\quad \left[\begin{matrix}0 & 1/3 \\ 1 & -1/3\end{matrix}\right]\]\[\Large X(2\pi)\quad=\quad \left[\begin{matrix}e^{2\pi} & e^{-2\pi} \\ 3e^{2\pi} & 0\end{matrix}\right]\]

The multiplication is like this:\[\Large B\quad=\quad X^{-1}(0)\cdot X(2\pi)\]
I seem to keep coming up with:\[\Large B\quad=\quad \left[\begin{matrix}0 & e^{2\pi} \\ e^{-2\pi} & 0\end{matrix}\right]\]

Answer 1

But the answer is supposed to be:\[\Large B\quad=\quad \left[\begin{matrix}e^{2\pi} & 0 \\ 0 & e^{-2\pi}\end{matrix}\right]\]

Heeeeeelp :(
Is there some rule that allows me to switch places like that?
Or am I just messing up the multiplication?

Answer 2

@dan815 @satellite73