Find all $2 \times 2$ matrices $A$ that have the property that for any $2 \times 2$ matrix $B$,
$A B = BA $.

Please help! Thank you!

Question

Find all $2 \times 2$ matrices $A$ that have the property that for any $2 \times 2$ matrix $B$,
$A B = BA $. 

Please help! Thank you!

anonymous · Answer

I believe this would be symmetric matrices.

anonymous · Answer

Just a hunch

anonymous · Answer

Symmetric matric matricies follow the pattern:$$
A = \begin{bmatrix}
a&b\b&c
\end{bmatrix}
$$

jim_thompson5910 · Answer

I'm no sure if this encapsulates all cases, but here is a condition where A*B = B*A http://math.stackexchange.com/questions/170241/when-is-matrix-multiplication-commutative

jim_thompson5910 · Answer

the user `Johannes Kloos` gives a good proof

jim_thompson5910 · Answer

sorry typo, I meant to say "not" instead of "no"

kainui · Answer

One way is to "brute force" it and write out two matrices and multiply them together in both ways and set the corresponding entries equal and see what pops out.