If A2 − A + I = O, where O is the zero matrix and I is the identity matrix, then A−1 is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → I − A
From the given equation:
\(A^2 - A + I = O\)
\(A - A^2 = I\)
\(A(I - A) = I\)
In the same way \((I - A)A = A - A^2 = I\). A matrix B with \(AB = BA = I\) is the inverse of A, so
\(A^{-1} = I - A\)