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If AB=BA then which of following are true?

1)(A+B)(A-B)=A^2-B^2

2)(AB)^n=A^n B^n

3)AB^n=B^n A

4)A=I or B=I

2 Answers

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AB = BA
AB^n = ABBBBBBBBBB........ //n times B

         = (AB)BBBBBBBB........

        = BABBBBBBBBBB....... // replace AB by BA

        = B(AB)BBBBBBBB....... repeat untill A reaches Rightmost possition..

 

AB^n = B^nA

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