If for the matrix A, A^3 = I, than A^ -1 = - Vidyadip

MCQ

If for the matrix $A, A^3 = I,$ than $A^{-1} =$

✓
$A^2$
B
$A^3$
C
$A$
D
None of these.

✓

Answer

Correct option: A.

$A^2$

$A^3 = I$
$\Rightarrow A^{-1}A^3 = A^{-1}I$
$\Rightarrow IA^2 = A^{-1}I$
$\Rightarrow A^2 = A^{-1}$

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