More Problems on Linear Systems and Matrices

Problem. Consider the matrix

\begin{displaymath}A = \left(\begin{array}{rrrr}
1 & -1 \\
2 & 1\\
\end{array} \right) \;.\end{displaymath}

Use systems to find all the 2x2 matrices $B$ such that

\begin{displaymath}A\;B = B\; A\end{displaymath}

Use this conclusion to find a matrix $C$ such that

\begin{displaymath}A\;C \neq C\; A\end{displaymath}

Answer.


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