JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If \(A\) is a \(3×3\) non-singular matrix such that \(AA’=A’A \) and \( B=A^{-1}A’\) then \(BB’ \) equals
- A \(B^{-1}\)
- B \(( B^{-1})’\)
- C \(I+B\)
- D \(I\)
Answer & Solution
Correct Answer
(D) \(I\)
Step-by-step Solution
Detailed explanation
\(AA' = A'A\) \(B = {A^{ - 1}}A'\) \(B' = A\left( {{A^{ - 1}}} \right)'\) \(B \cdot B' = {A^{ - 1}}\left( {A'A} \right)\left( {{A^{ - 1}}} \right)'\) \( = {A^{ - 1}}\left( {AA'} \right)\left( {{A^{ - 1}}} \right)1\)…
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