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## Main Question or Discussion Point

Let D =

[d11 d12]

[d21 d22]

be a 2x2 matrix. Prove that D commutes with all other 2x2

matrices if and only if d12 = d21 = 0 and d11 = d22.

I know if we can prove for every A, AD=DA should be true, but I really dont know how to proceed from there. I tried equating elements of AD with DA but that really didnt help.

Can anyone help me with this problem. Thanks..

[d11 d12]

[d21 d22]

be a 2x2 matrix. Prove that D commutes with all other 2x2

matrices if and only if d12 = d21 = 0 and d11 = d22.

I know if we can prove for every A, AD=DA should be true, but I really dont know how to proceed from there. I tried equating elements of AD with DA but that really didnt help.

Can anyone help me with this problem. Thanks..