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Determinants — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDeterminants1 Mark
MCQ
If a matrix $A$ is such that $3 A^3+2 A^2+5 A+1=0$, then $A^{-1}$ equal to:
  • A
    $-\left(3 A^2+2 A+5\right)$
  • B
    $3 A^2+2 A+5$
  • C
    $3 A^2-2 A-5$
  • ✓
    None of these.
✓

Answer

Correct option: D.
None of these.
$3 A^3+2 A^2+5 A+I=0$
$\Rightarrow 3 A^{-1} A^3+2 A^{-1} A^2+5 A^{-1} A+A^{-1} I=A^{-1} 0$
$\Rightarrow 3 A^2+2 A+5 I+A^{-1}=0$
$\Rightarrow A^{-1}=-\left(3 A^2+2 A+5 I\right)$

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