Question

If \(A\) is a non-singular matrix and \(A^2-A+I = 0\), then \(A^{-1} = \ldots\)

• A. \(A\)
• B. \(A-I\)
• C. \(I-A\)
• D. \(A+I\)

Hint:

Multiply the given relation by \(A^{-1}\).

Answer 1

The Correct Option is C

Step 1: Factor
$A^2-A+I=0$ gives $A(A-I)=-I$, so $A(I-A)=I$.

Step 2: Read the inverse
A matrix whose product with $A$ is $I$ is the inverse, so $A^{-1}=I-A$, option (C).

Final Answer:
$A^{-1}=I-A$, option (C). \[ \boxed{I-A} \]