If \(A=\begin{bmatrix}1 & -1 & 2\\ -2 & 2 & -4\\ 0 & 2 & 9\end{bmatrix}\) then \(A^{-1}\) is equal to.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → does not exist
A square matrix has an inverse only when it is non-singular, that is, \(|A| \ne 0\).
The first two rows of A are:
\(R_1 = (1,\ -1,\ 2)\)
\(R_2 = (-2,\ 2,\ -4) = -2\,R_1\)
A determinant with two proportional rows is zero, so
\(|A| = 0\)
A is singular, so \(A^{-1}\) does not exist.