Let $a$ and $b$ be real numbers. Considere the $2\times 2$ matrix \begin{equation*}A=\left[\begin{array}{cc}a&b\\-b&a\end{array}\right]. \end{equation*} What is the centralizer of the matrix $A$ in $M_2(\mathbb R)$?
Matrices that Commute with of a Specific matrix
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linear-algebra
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4Have you tried working it out from the definition? – 2012-09-26