If A^2 - A + I = 0, then A^ - 1 = - Vidyadip

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
(c) ${A^2} - A + I = 0$

==> $I = A - {A^2} \Rightarrow $$I = A(I - A)$

==> ${A^{ - 1}}I = {A^{ - 1}}(A(I - A))$ $ \Rightarrow $ ${A^{ - 1}} = I - A$.

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