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When Does 2x2 Matrix FOIL Work?

LINALG-CZVJNK

For which of the following pairs of matrices $A$ and $B$ is the equation:

$$(A+B)^2=A^2+2AB+B^2$$

...TRUE?

Select ALL that apply.

A

$A=\begin{pmatrix}1&0\\\ 0&2\end{pmatrix}$, $B=\begin{pmatrix}1&1\\\ 0&1\end{pmatrix}$

B

$A=\begin{pmatrix}1&2\\\ 3&4\end{pmatrix}$, $B=\begin{pmatrix}0&-1\\\ 1&0\end{pmatrix}$

C

$A=\begin{pmatrix}0&-1\\\ 1&0\end{pmatrix}$, $B=\begin{pmatrix}1&\sqrt{3}\\\ -\sqrt{3}&1\end{pmatrix}$

D

$A=\begin{pmatrix}3&0\\\ 0&2\end{pmatrix}$, $B=\begin{pmatrix}-1&0\\\ 0&1\end{pmatrix}$