JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(A=\left[a_{i j}\right]\) be a real matrix of order \(3 \times 3\), such that \(a_{i 1}+a_{i 2}+a_{i 3}=1\), for \(i=1,2,3\). Then, the sum of all the entries of the matrix \(A^{3}\) is equal to:
- A \(1\)
- B \(2\)
- C \(3\)
- D \(9\)
Answer & Solution
Correct Answer
(C) \(3\)
Step-by-step Solution
Detailed explanation
\(A=\left[\begin{array}{lll}a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array}\right]\) Let \(x=\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right]\)…
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