JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(S\) be the set containing all \(3 \times 3\) matrices with entries from \(\{-1,0,1\}\). The total number of matrices \(A \in S\) such that the sum of all the diagonal elements of \(A ^{ T } A\) is \(6\) is.
- A \(5376\)
- B \(5377\)
- C \(5369\)
- D \(5362\)
Answer & Solution
Correct Answer
(A) \(5376\)
Step-by-step Solution
Detailed explanation
\(\operatorname{Tr}\left(A A^{T}\right)=6\) \(AA ^{ T }=\left[\begin{array}{lll} a & d & g \\ b & e & h \\ c & f & i \end{array}\right]\left[\begin{array}{lll} a & b & c \\d & e & f \\ g & h & i \end{array}\right]\) Now given…
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