JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If \(A=\left[\begin{array}{cc}2 & 3 \\ 0 & -1\end{array}\right],\) then the value of \(\operatorname{det}\left( A ^{4}\right)+\operatorname{det}\left( A ^{10}-(\operatorname{Adj}(2 A ))^{10}\right)\) is equal to ........
- A \(9\)
- B \(25\)
- C \(16\)
- D \(12\)
Answer & Solution
Correct Answer
(C) \(16\)
Step-by-step Solution
Detailed explanation
\(2 A\) adj \((2 A )=|2 A | I\) \(\Rightarrow A\) adj \((2 A )=-4 I\) \(......(I)\) Now, \(E =\left| A ^{4}\right|+\mid A ^{10}-(\operatorname{adj}(2 A ))^{10}\) \(=(-2)^{4}+\frac{\left| A ^{20}- A ^{10}(\operatorname{adj} 2 A )^{10}\right|}{| A |^{10}}\)…
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