A=ai,j, B=bi,jAB−BA=(a1,2b2,1−a2,1b1,2(a1,1−a2,2)b1,2+a1,2(b2,2−b1,1)(a2,2−a1,1)b2,1+a2,1(b1,1−b2,2)a2,1b1,2−a1,2b2,1)=0
From the first row we see a1,2=a2,1=0Then from row 2, a1,1=a2,2This agrees with row 3, and row 4 agrees with row 1 A=λI2,2, λ∈C
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