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  4. If A is a square matrix such that (A - 2I) (A + I) = 0, then A-1 =

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Q. If A is a square matrix such that (A - 2I) (A + I) = 0, then $A^{-1}$ =

Determinants

Solution:

$\left(A - 2I\right)\left(A +I\right) = 0$
$ \Rightarrow AA - A - 2 I = 0 \left(\because AI = A\right) $
$\Rightarrow A \left(\frac{A-I}{2}\right) = I \therefore \frac{A-I}{2} = A^{-1} $