We have a matrix $A=\begin{pmatrix}1&2\\3&4\end{pmatrix}$. And I am looking for the set $\text{Com}(A) = \{B \in M_2 | AB = BA\}$.
2026-04-05 18:35:08.1775414108
Finding the set $\text{com}(A)$ where $AB= BA$
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Hint: Let $B=\begin{pmatrix}a&b\\c&d\end{pmatrix}$. Then $$AB=BA \text{ becomes } \begin{pmatrix}1&2\\3&4\end{pmatrix}\begin{pmatrix}a&b\\c&d\end{pmatrix}=\begin{pmatrix}a&b\\c&d\end{pmatrix}\begin{pmatrix}1&2\\3&4\end{pmatrix}.$$ Do the matrix multiplication and solve the resulting simultaneous equations.