JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(A=\left[\begin{array}{cc}2 & -1 \\ 1 & 1\end{array}\right]\). If the sum of the diagonal elements of \(\mathrm{A}^{13}\) is \(3^{\mathrm{n}}\), then \(\mathrm{n}\) is equal to ..........
- A \(7\)
- B \(9\)
- C \(6\)
- D \(1\)
Answer & Solution
Correct Answer
(A) \(7\)
Step-by-step Solution
Detailed explanation
\(A=\left[\begin{array}{cc}2 & -1 \\ 1 & 1\end{array}\right]\) \(A^2=\left[\begin{array}{cc}2 & -1 \\ 1 & 1\end{array}\right]\left[\begin{array}{cc}2 & -1 \\ 1 & 1\end{array}\right]=\left[\begin{array}{cc}3 & -3 \\ 3 & 0\end{array}\right]\)…
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