JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(A\) be a \(2 \times 2\) matrix with real entries such that \(A ^{\prime}=\alpha A + I\), where \(\alpha \in R -\{-1,1\}\). If det \(\left(A^2-A\right)=4\), then the sum of all possible values of \(\alpha\) is equal to
- A \(0\)
- B \(\frac{3}{2}\)
- C \(\frac{5}{2}\)
- D \(2\)
Answer & Solution
Correct Answer
(C) \(\frac{5}{2}\)
Step-by-step Solution
Detailed explanation
\(A ^{ T }=\alpha A + I\) \(A =\alpha A ^{ T }+ I\) \(A =\alpha(\alpha A + I )+ I\) \(A =\alpha^2 A +(\alpha+1) I\) \(A \left(1-\alpha^2\right)=(\alpha+1) I\) \(A =\frac{ I }{1-\alpha}\) \(| A |=\frac{1}{(1-\alpha)^2}\) \(\left| A ^2- A \right|=| A || A - I |\)…
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