JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
The number of elements in the set \(\left\{A=\left(\begin{array}{ll}a & b \\ 0 & d\end{array}\right): a, b, d \in\{-1,0,1\}\right.\) and \(\left.(I-A)^{3}=I-A^{3}\right\}\) where \(I\) is \(2 \times 2\) identity matrix, is :
- A \(8\)
- B \(10\)
- C \(11\)
- D \(12\)
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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