Let A, B, and C be real 2×2 matrices and denote A⋅B−B⋅A by [A, B]. Prove that: [A, A]=0

Pertanyaan

Let begin mathsize 14px style A end stylebegin mathsize 14px style B end style, and begin mathsize 14px style C end style be real begin mathsize 14px style 2 cross times 2 end style matrices and denote begin mathsize 14px style A times B minus B times A end style by begin mathsize 14px style left square bracket A comma space B right square bracket end style. Prove that:

begin mathsize 14px style left square bracket A comma space A right square bracket equals 0 end style 

A. Septianingsih

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Pembahasan

table attributes columnalign right center left columnspacing 0px end attributes row straight A equals cell open parentheses table row straight a straight b row straight c straight d end table close parentheses end cell row cell open square brackets straight A comma straight A close square brackets end cell equals cell straight A. straight A minus straight A. straight A end cell row blank equals cell open parentheses table row straight a straight b row straight c straight d end table close parentheses squared minus open parentheses table row straight a straight b row straight c straight d end table close parentheses squared end cell row blank equals cell 0 space left parenthesis terbukti right parenthesis end cell end table 

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Let A, B, and C be real 2×2 matrices and denote A⋅B−B⋅A by [A, B]. Prove that: [[A,B], C]+[[B, C], A]+[[C, A], B]=0

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