JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
The number of all \(3 \times 3\) matrices \(A\), with enteries from the set \(\{-1,0,1\}\) such that the sum of the diagonal elements of \(\mathrm{AA}^{\mathrm{T}}\) is \(3,\) is
- A \(632\)
- B \(672\)
- C \(682\)
- D \(638\)
Answer & Solution
Correct Answer
(B) \(672\)
Step-by-step Solution
Detailed explanation
\(\operatorname{trace}\left(\mathrm{AA}^{\mathrm{T}}\right)=\Sigma \mathrm{a}_{\mathrm{ij}}^{2}=3\) Hence, number of such matrices \(=^{9} \mathrm{C}_{3} \times 2^{3}=672.00\)
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