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Matrics — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsMatrics2 Marks
MCQ
If for the matrix $A, A^3=I$, then $A^{-1}=$
  • ✓
    $A ^2$
  • B
    $A ^3$
  • C
    A
  • D
    none of these
✓

Answer

Correct option: A.
$A ^2$
(A) $A ^3= I$
$\Rightarrow A ^{-1} A^3= A ^{-1} \cdot I$
$\Rightarrow\left( A ^{-1} A\right) A ^2= A ^{-1}$
$\Rightarrow IA ^2= A ^{-1} \Rightarrow A^2= A ^{-1}$

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