Proving a matrix

[mahjk17]

Well, let me start off by saying that I never done a matrix proof nor did my professor teach us so I am coming here for help. The question is, "show that if D =

is a 2x2 diagonal matrix where 'a' does not equal 'b', then the only matrices that commute (under matrix multiplication) with D are other 2x2 diagonal matrices." Any help or inquiry will be greatly appreciated.

 

[daon2]

Show that the following is true (assuming a=/= b):

\(\displaystyle {w \,\, x \choose y \,\, z}{a \,\, 0 \choose 0 \,\, b}={a \,\, 0 \choose 0 \,\, b}{w \,\, x \choose y \,\, z}\)

If and only if x=0 and y=0. Hint: Multiply both sides out and equate the four components.

 

[mahjk17]

Thank you very much Daon2!! I understand now!