JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \( A=\begin{bmatrix}0&2&-3\\ -2&0&1\\ 3&-1&0\end{bmatrix} \) and B be a matrix such that \( B(I-A)=I+A \). Then the sum of the diagonal elements of \( B^{T}B \) is equal to:
- A 1
- B 2
- C 3
- D 0
Answer & Solution
Correct Answer
(C) 3
Step-by-step Solution
Detailed explanation
\( A^T = -A \) \(B =( I + A )( I - A )^{-1}\) \(B ^{ T }=\left(( I - A )^{-1}\right)^{ T }( I + A )^{ T }\) \(B^T=\left(I-A^T\right)^{-1}\left(I+A^T\right)\) \(B ^{ T }=( I + A )^{-1}( I + A )\) \(B ^{ T } B =( I + A )^{-1}( I - A )( I + A )( I - A )^{-1}\)…
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