Find all matrices commuting with

> A:=Matrix([[1,0],[0,2]]);

> B:=Matrix([[a,b],[c,d]]);

> A.B;

> B.A;

> A.B-B.A;

AB=BA <=> AB-BA=0 <=> b=0 且 c=0 <=> B 是對角化矩陣 

,so we get B=

讓 我們驗證一下

> C:=Matrix([[a,0],[0,d]]);

> A.C-C.A;

故 得證