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Matrics — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsMatrics2 Marks
MCQ
If $A ^2- A + I =0$, then $A ^{-1}=$
  • A
    $A^{-2}$
  • B
    $A + I$
  • ✓
    $I - A$
  • D
    $A - I$
✓

Answer

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

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