A) \[I+B\]
B) \[I\]
C) \[{{B}^{-1}}\]
D) \[({{B}^{-1}})'\]
Correct Answer: B
Solution :
\[BBT=\left( {{A}^{-1}}{{A}^{T}} \right){{\left( {{A}^{-1}}{{A}^{T}} \right)}^{T}}\]\[={{A}^{-1}}.\left( {{A}^{T}}A \right){{\left( {{A}^{-1}} \right)}^{T}}\] \[=\left( {{A}^{-1}}A \right){{A}^{T}}.{{\left( {{A}^{-1}} \right)}^{T}}\] \[={{\left( {{A}^{-1}}A \right)}^{T}}=I\] | \[=\left( {{A}^{-1}}{{A}^{T}} \right)\left( A\cdot {{\left( {{A}^{-1}} \right)}^{T}} \right)\] \[={{A}^{-1}}\left( A{{A}^{T}} \right){{\left( {{A}^{-1}} \right)}^{T}}\] \[={{A}^{T}}.{{\left( {{A}^{-1}} \right)}^{T}}\] |
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