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Find a 3x3 matrix A such that \( \mathbf A\begin{pmatrix} a & b & c \\ d & e & f \\ g & h & i \end{pmatrix} = \begin{pmatrix} g & h & i \\ a & b & c \\ d & e & f \end{pmatrix}.\)

 

I don't really know where to start because I can't wrap my head around the fact that the letters switch. Help, please!

 

Also, don't solve the problem for me because I want to figure it out myself. Just a few hints please :)

 May 19, 2022
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By elementary row operations,

 

\(\mathbf{A} = \begin{pmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \end{pmatrix}\)

 May 19, 2022

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