If $A=\begin{bmatrix}1 & -1 & 2

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Matrices

Question:

If $A=\begin{bmatrix}1 & -1 & 2 \\-2 & 2 & -4\\0 & 2 & 9\end{bmatrix}$ then $A^{-1}$ is equal to.

Options:

$\begin{bmatrix}2 & -2 & 4 \\0 & 2 & 9\\-1 & 1 & -2\end{bmatrix}$

does not exist

$\begin{bmatrix}0 & 2 & 9\\1 & -1 & 2\\-2 & 2 & -4\end{bmatrix}$

$\begin{bmatrix}1 & -2 & 0 \\-1 & 2 & 2\\2 & -4 & 9\end{bmatrix}$

Correct Answer:

does not exist

Explanation:

The correct answer is option (2) → does not exist $\frac{80}{89}$

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