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Linear Algebra

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Which Matrices Commute

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Each choice is a pair of two $2\times2$ matrices, $A$ and $B$.

Which of these pairs multiplicatively commute?

Select ALL that apply.

A

$A=\begin{pmatrix}1&2\\\ 3&4\end{pmatrix}$, $B=\begin{pmatrix}4&3\\\ 2&1\end{pmatrix}$

B

$A=I_2$, $B=\begin{pmatrix}1&2\\\ 3&4\end{pmatrix}$

C

$A$ is the standard matrix of reflection about the $x$-axis, $B$ is the standard matrix of reflection about the $y$-axis

D

$A$ is clockwise rotation by $\pi$, $B$ is counter-clockwise rotation by $\pi/4$

E

$A=\begin{pmatrix}1&1\\\ 0&1\end{pmatrix}$, $B=\begin{pmatrix}1&0\\\ 1&1\end{pmatrix}$