A proof related to 2 X 2 matrix

[Ampatishan]

Let A be a 2 X 2 matrix such that AX = XA for all 2 X 2 real matrices X. Show that A =kI for some k belonging to R

 

[berkeman]

Let A be a 2 X 2 matrix such that AX = XA for all 2 X 2 real matrices X. Show that A =kI for some k belonging to R

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