JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let the matrix \(A =\left[\begin{array}{lll}0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0\end{array}\right]\) and the matrix \(B _{0}= A ^{49}+2 A ^{98}\). If \(B _{ n }= Adj \left( B _{ n -1}\right)\) for all \(n \geq 1\),then \(\operatorname{det}\left( B _{4}\right)\) is equal to.
- A \(3^{28}\)
- B \(3^{30}\)
- C \(3^{32}\)
- D \(3^{36}\)
Answer & Solution
Correct Answer
(C) \(3^{32}\)
Step-by-step Solution
Detailed explanation
\(A ^{2}=\left[\begin{array}{lll}0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0\end{array}\right]\left[\begin{array}{lll}0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0\end{array}\right]\) \(=\left[\begin{array}{lll}0 & 0 & 1 \\1 & 0 & 0 \\0 & 1 & 0\end{array}\right]\) \(a \leftrightarrow R _{2}\)…
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