Q63 / 150 · MHT CET 2026 (17 April Shift 1) · Mathematics
If $A$ is a non-singular matrix and $A^2 - A + I = 0$, then $A^{-1} = \ldots$
- A$A$
- B$A - I$
- Correct answerC$I - A$
- D$A + I$
Solution
Given $A^2 - A + I = 0$
Multiplying both sides by $A^{-1}$, we get
$A^{-1}(A^2 - A + I) = 0$
$A - I + A^{-1} = 0$
$A^{-1} = I - A$
Answer: $I - A$
Multiplying both sides by $A^{-1}$, we get
$A^{-1}(A^2 - A + I) = 0$
$A - I + A^{-1} = 0$
$A^{-1} = I - A$
Answer: $I - A$
Hence, the correct answer is option: 'C'.