A) \[{{A}^{-n}}{{B}^{n}}{{A}^{n}}\]
B) \[{{A}^{n}}{{B}^{n}}{{A}^{-n}}\]
C) \[{{A}^{-1}}{{B}^{n}}A\]
D) \[{{A}^{-n}}B{{A}^{n}}\]
Correct Answer: C
Solution :
for \[n=2\] \[\Rightarrow ({{A}^{-1}}BA)\,\,({{A}^{-1}}BA)={{A}^{-1}}{{B}^{2}}A\] \[{{({{A}^{-1}}BA)}^{3}}={{({{A}^{-1}}BA)}^{2}}\,\,({{A}^{-1}}BA)=({{A}^{-1}}{{B}^{2}}A)\,\,({{A}^{-1}}BA)\]\[={{A}^{-1}}{{B}^{3}}A\]and so on thus \[{{({{A}^{-1}}BA)}^{n}}\] \[={{A}^{-1}}{{B}^{n}}A\]You need to login to perform this action.
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