If \(A^2-A+I=O\), then \(A^{-1}\) is equal to:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(I-A\)
Here O is the zero matrix. From the given equation,
\(A - A^2 = I\)
Taking A out as a common factor on the left:
\(A(I - A) = I\)
In the same way \((I - A)A = A - A^2 = I\). A matrix B with AB = BA = I is the inverse of A, so A is invertible and
\(A^{-1} = I - A\)