Question

answer the following question ​

Answer 1

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It  is given that    

                               B = -A^-1(BA)

          now, pre-multiplying by A on both sides, we will get

                                AB = -BA

                               AB+BA = 0.........................(1)

Now coming to the problem:

(A+B)2=(A+B)*(A+B)  =  A^2+B^2+AB+BA.....................(2)

from (1) and (2), (SUBSTITUTING AB= -BA)  we get

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

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