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  • If A, B are square matrices of the same order such that (A+B)(A-B)=A^2-B^2, then (ABA^-1)^2 equals

If A, B are square matrices of the same order such that (A+B)(A-B)=A^2-B^2, then (ABA^-1)^2 equals

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Solution: 

            (A+B)(A-B)=A^2-B^2 gives  AB=BA

          Now ,    (ABA^-1)^2=(ABA^-1)(ABA^-1)

                           (ABA^-1)^2=AB(A^-1A)BA^-1=B^2

                              

 

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Deependra Verma

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