Elementary row transformations can be used to find Inverse for any square matrix.

True

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False

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Solution

The correct option is B
False

Even with using Elementary row transformations Inverse can be found only when determinant of the given square matrix is not 0. In such case we usually won’t be able to convert the given matrix to identity matrix using Elementary row transformations any number of times.

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Elementary row transformations can be used to find Inverse for any square matrix.

⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 2 & 5 & 7 - 2 & - 4 & 5 \end{matrix} ⎤ ⎥ ⎦

A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & - 2 - 1 & 3 & 0 0 & - 2 & 1 \end{matrix} ⎤ ⎥ ⎦

A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 2 & 5 & 7 - 2 & - 4 & - 5 \end{matrix} ⎤ ⎥ ⎦

A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 2 & 5 & 7 - 2 & - 4 & - 5 \end{matrix} ⎤ ⎥ ⎦

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