JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(S=\left\{n \in N \mid\left(\begin{array}{ll}0 & i \\ 1 & 0\end{array}\right)^{n}\left(\begin{array}{ll}a & b \\ c & d\end{array}\right)=\left(\begin{array}{ll}a & b \\ c & d\end{array}\right) \forall a, b, c, d \in R\right\}\), where \(i=\sqrt{-1} .\) Then the number of \(2 -\) digit numbers in the set \(\mathrm{S}\) is \(......\)
- A \(11\)
- B \(15\)
- C \(19\)
- D \(21\)
Answer & Solution
Correct Answer
(A) \(11\)
Step-by-step Solution
Detailed explanation
Lex \(X=\left(\begin{array}{ll}a & b \\ c & d\end{array}\right) \;and\; A=\left(\begin{array}{ll}0 & i \\ 1 & 0\end{array}\right)^{n}\) \(\Rightarrow \mathrm{AX}=\mathrm{IX}\) \(\Rightarrow \mathrm{A}=\mathrm{I}\)…
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