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The trace tr ( A ) of a matrix A = ( a 11 ​ a 21 ​ ​ a 12 ​ a 22 ​ ​ ) is defined by tr ( A ) = a 11 ​ + a 22 ​ . Prove that: tr ( A ⋅ B ) = tr ( B ⋅ A )

The trace  of a matrix  is defined by . Prove that:

   

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A. Septianingsih

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Pembahasan

table attributes columnalign right center left columnspacing 0px end attributes row B equals cell open parentheses table row cell b subscript 11 end cell cell b subscript 12 end cell row cell b subscript 21 end cell cell b subscript 22 end cell end table close parentheses end cell row cell t r left parenthesis A. B right parenthesis end cell equals cell t r left parenthesis B. A right parenthesis end cell row cell t r open square brackets open parentheses table row cell a subscript 11 end cell cell a subscript 12 end cell row cell a subscript 21 end cell cell a subscript 22 end cell end table close parentheses open parentheses table row cell b subscript 11 end cell cell b subscript 12 end cell row cell b subscript 21 end cell cell b subscript 22 end cell end table close parentheses close square brackets end cell equals cell t r open square brackets open parentheses table row cell b subscript 11 end cell cell b subscript 12 end cell row cell b subscript 21 end cell cell b subscript 22 end cell end table close parentheses open parentheses table row cell a subscript 11 end cell cell a subscript 12 end cell row cell a subscript 21 end cell cell a subscript 22 end cell end table close parentheses close square brackets end cell row cell t r open parentheses table row cell a subscript 11. b subscript 11 plus a subscript 12. b subscript 21 end cell cell a subscript 11. b subscript 12 plus a subscript 12. b subscript 22 end cell row cell a subscript 21. b subscript 11 plus a subscript 22. b subscript 21 end cell cell a subscript 21. b subscript 12 plus b subscript 11. b subscript 22 end cell end table close parentheses end cell equals cell t r open parentheses table row cell b subscript 11. a subscript 11 plus b subscript 12. a subscript 21 end cell cell b subscript 11. a subscript 12 plus b subscript 12. a subscript 22 end cell row cell b subscript 21. a subscript 11 plus b subscript 22. a subscript 21 end cell cell b subscript 21. a subscript 12 plus b subscript 22. a subscript 22 end cell end table close parentheses end cell row cell a subscript 11. b subscript 11 plus a subscript 12. b subscript 21 plus a subscript 21. b subscript 12 plus b subscript 11. b subscript 22 end cell equals cell b subscript 11. a subscript 11 plus b subscript 12. a subscript 21 plus b subscript 21. a subscript 12 plus b subscript 22. a subscript 22 end cell row cell a subscript 11. b subscript 11 plus a subscript 12. b subscript 21 plus a subscript 21. b subscript 12 plus b subscript 11. b subscript 22 end cell equals cell a subscript 11. b subscript 11 plus a subscript 12. b subscript 21 plus a subscript 21. b subscript 12 plus b subscript 11. b subscript 22 end cell row blank blank cell left parenthesis T e r b u k t i right parenthesis end cell end table 

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