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Matrics — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsMatrics2 Marks
MCQ
If a matrix $A$ is such that $4 A^3+2 A^2+7 A+I=0$, then $A^{-1}$ equals
  • A
    $4 A^2+2 A+71$
  • ✓
    $-\left(4 A^2+2 A+71\right)$
  • C
    $-\left(4 A^2-2 A+71\right)$
  • D
    $4 A^2+2 A-71$
✓

Answer

Correct option: B.
$-\left(4 A^2+2 A+71\right)$
(B) $4 A^3+2 A^2+7 A+I=0$
$\Rightarrow 4 A^{-1} A^3+2 A^{-1} A^2+7 A^{-1} A+ A ^{-1} I =0$
$\Rightarrow 4 A^2+2 A+7 I + A ^{-1}=0$
$\Rightarrow A^{-1}=-\left(4 A^3+2 A+7 I\right)$

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