Answer:
We have, \[B=-\,{{A}^{-1}}BA\] \[\Rightarrow \] \[AB=-A({{A}^{-1}}BA)=-\,(A{{A}^{-1}})(BA)\] \[=-\,(l)(BA)=-\,BA\] \[\Rightarrow \] \[AB+BA=0\] Now, \[{{(A+B)}^{2}}=(A+B)(A+B)={{A}^{2}}+AB+BA+{{B}^{2}}\] \[={{A}^{2}}+0+{{B}^{2}}\] \[[\because \,\,\,AB=-AB]\] \[={{A}^{2}}+{{B}^{2}}\]
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