If \(A\) is a \(3\times3\) non-singular matrix such that \(AA'=A'A\) and \(B=A^{-1}A'\), then \(BB'\) equals :
Show Hint
- \(B^{-1}\)
- \((B^{-1})'\)
- \(I+B\)
- \(I\)
The Correct Option is D
Solution and Explanation
\(BB'=A^{-1}A'\,A\,(A')^{-1}=A^{-1}(A'A)(A')^{-1}\).
Using \(A'A=AA'\): \(BB'=A^{-1}(AA')(A')^{-1}=(A^{-1}A)(A'(A')^{-1})=I\cdot I=I\).
Answer: (4) \(I\)
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