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JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant

ગણ \(\left\{A=\left(\begin{array}{ll}a & b \\ 0 & d\end{array}\right): a, b, d \in\{-1,0,1\}\right.\) અને \(\left.(I-A)^{3}=I-A^{3}\right\}\) ની સભ્ય સંખ્યા મેળવો. કે જ્યાં \(I\) એ  \(2 \times 2\) એકમ શ્રેણિક છે.

  1. A \(8\)
  2. B \(10\)
  3. C \(11\)
  4. D \(12\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(8\)

Step-by-step Solution

Detailed explanation

\((\mathrm{I}-\mathrm{A})^{3}=\mathrm{I}^{3}-\mathrm{A}^{3}-3 \mathrm{~A}(\mathrm{I}-\mathrm{A})=\mathrm{I}-\mathrm{A}^{3}\) \(\Rightarrow 3 \mathrm{~A}(\mathrm{I}-\mathrm{A})=0 \text { or } \mathrm{A}^{2}=\mathrm{A}\)…
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