JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(S=\left\{\left(\begin{array}{cc}-1 & a \\ 0 & b\end{array}\right) ; a, b \in\{1,2,3, \ldots 100\}\right\}\) and let \(T_{n}=\left\{A \in S: A^{n(n+1)}=I\right\}\). Then the number of elements in \(\bigcap \limits_{n=1}^{100} T_{n}\) is
- A \(50\)
- B \(85\)
- C \(100\)
- D \(137\)
Answer & Solution
Correct Answer
(C) \(100\)
Step-by-step Solution
Detailed explanation
\(A=\left[\begin{array}{cc}-1 & a \\ 0 & b\end{array}\right]\) \(A^{2}=\left[\begin{array}{cc}-1 & a \\ 0 & b\end{array}\right]\left[\begin{array}{cc}-1 & a \\ 0 & b\end{array}\right]\) \(=\left[\begin{array}{cc}1 & -a+a b \\ 0 & b^{2}\end{array}\right]\)…
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