JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(A=\left[a_{i j}\right]_{2 \times 2}\) where \(a_{i j} \neq 0\) for all \(i, j\) and \(A^2=I\). Let a be the sum of all diagonal elements of \(A\) and \(b =| A |\), then \(3 a ^2+4 b ^2\) is equal to
- A \(7\)
- B \(14\)
- C \(3\)
- D \(4\)
Answer & Solution
Correct Answer
(D) \(4\)
Step-by-step Solution
Detailed explanation
\begin{aligned}& \text { Let } A=\left[\begin{array}{ll} p & l \\r & s\end{array}\right] \\& A^2=\left[\begin{array}{ll} p ^2+ qr & pq + qs \\pr + rs & qs + s ^2\end{array}\right] \\& \Rightarrow p ^2+ qr =1(1) pq + qs =0 \Rightarrow q ( p + s )=0 \\& \Rightarrow s ^2+ qr =1(2)…
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