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Question

Find inverse, by elementary row operations (if possible), of the following matrices
$$\begin{bmatrix} 1 & -3 \\ -2 & 6 \end{bmatrix}$$


Solution

To check if the inverse exist we find the determinant:
We have:
$$A=\begin{bmatrix}
 1 & -3 \\
 -2 & 6
\end{bmatrix}$$

So, $$\left|A\right|=1\times 6-(-2\times -3)$$

$$\Rightarrow \left|A\right|=6-6=0$$

Since, $$|A|=0$$, hence the inverse does not exist

Mathematics

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