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Adjoint and Inverse of a Matrix — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSAdjoint and Inverse of a Matrix1 Mark
MCQ
If a matrix $A$ is such that $3A^3 + 2A^2 + 5A + I = 0,$ then $A^{-1}$ equal to:
  • ✓
    $-(3A^2 + 2A + 5)$
  • B
    $3A^2 + 2A + 5$
  • C
    $3A^2 - 2A - 5$
  • D
    None of these.
✓

Answer

Correct option: A.
$-(3A^2 + 2A + 5)$
$3A^3 + 2A^2 + 5A + I = 0$
$\Rightarrow 3A^{-1} A^3 + 2A^{-1}A^2 + 5A^{-1}A + A^{-1 }I = A^{-1}0$
$\Rightarrow 3A^2 + 2A + 5I + A^{-1} = 0$
$\Rightarrow A^{-1} = -(3A^2 + 2A + 5I)$

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