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