First slide

Applications of determinant

Question

A square non-singular matrix A satisfies $A^{2} - A + 2 I = 0$ , then $A^{- 1}$ =

Easy

A

$I - A$
B

$\frac{1}{2} (I - A)$
C

$I + A$
D

$\frac{1}{2} (I + A)$

Solution

$A^{2} - A + 2 I = 0$
${Right multiplication with A}^{- 1}$
$\Rightarrow A - I + 2 A^{- 1} = 0$
$\Rightarrow A^{- 1} = \frac{1}{2} (I - A)$

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