JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(A=\begin{bmatrix}3&-4\\ 1&-1\end{bmatrix}\) and B be two matrices such that \(A^{100}=100B+I.\) Then the sum of all the elements of \(B^{100}\) is ___ .
- A 0
- B 100
- C 1
- D -1
Answer & Solution
Correct Answer
(A) 0
Step-by-step Solution
Detailed explanation
\(A=I+\left[\begin{array}{ll}2 & -4 \\ 1 & -2\end{array}\right]\), let \(M=\left[\begin{array}{ll}2 & -4 \\ 1 & -2\end{array}\right]\) \(M ^2=\left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right]= M ^3= M ^4=\ldots= M ^{100}\)…
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