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If $A=\begin{bmatrix}1 & -1 & 2 \\-2 & 2 & -4\\0 & 2 & 9\end{bmatrix}$ then $A^{-1}$ is equal to. |
$\begin{bmatrix}2 & -2 & 4 \\0 & 2 & 9\\-1 & 1 & -2\end{bmatrix}$ does not exist $\begin{bmatrix}0 & 2 & 9\\1 & -1 & 2\\-2 & 2 & -4\end{bmatrix}$ $\begin{bmatrix}1 & -2 & 0 \\-1 & 2 & 2\\2 & -4 & 9\end{bmatrix}$ |
does not exist |
The correct answer is option (2) → does not exist In $A=\begin{bmatrix}1 & -1 & 2 \\-2 & 2 & -4\\0 & 2 & 9\end{bmatrix}$ $R_2=-2R_1$ (proportional) $⇒|A|=0$ $⇒A^{-1}$ does not exist |
