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Let's say I have a matrix

\begin{bmatrix}a&b\\c&d\end{bmatrix}

What would I have the multiply the matrix above by to obtain the following?

**\begin{bmatrix}c&d\\a&b\end{bmatrix}

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  • $\begingroup$ Hmm, I see you may just have meant to multiply the given matrix by another matrix, not use Gauss Jordan operations. Is that what you meant? [If so I'll delete my irrelevant answer below...] $\endgroup$ – coffeemath Feb 5 '16 at 0:50
  • $\begingroup$ yes, that is what I meant. $\endgroup$ – Yunae Feb 5 '16 at 3:22
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We want $$\begin{bmatrix}A&B\\C&D\end{bmatrix}\begin{bmatrix}a&b\\c&d\end{bmatrix}=\begin{bmatrix}c&d\\a&b\end{bmatrix}$$ This means $c=Aa+Bc$, $d=Ab+Bd$, $a=Ca+Dc$, and $b=bC+Dd$. Suggestion: $$\begin{bmatrix}A&B\\C&D\end{bmatrix}=\begin{bmatrix}0&1\\1&0\end{bmatrix}$$

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The answer is going to be a matrix of zeroes and ones, since you just want to move the elements around, not scale them. Try some of the following and see what works:

$$\begin{bmatrix}1&1\\1&1\end{bmatrix}\\ \begin{bmatrix}1&0\\0&1\end{bmatrix}\\ \begin{bmatrix}1&0\\1&0\end{bmatrix}\\ \begin{bmatrix}0&1\\1&0\end{bmatrix}\\ \begin{bmatrix}0&0\\1&1\end{bmatrix}$$

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