## Condition that Two Matrices are Row Equivalent

## Problem 248

We say that two $m\times n$ matrices are **row equivalent** if one can be obtained from the other by a sequence of elementary row operations.

Let $A$ and $I$ be $2\times 2$ matrices defined as follows.

\[A=\begin{bmatrix}

1 & b\\

c& d

\end{bmatrix}, \qquad I=\begin{bmatrix}

1 & 0\\

0& 1

\end{bmatrix}.\]
Prove that the matrix $A$ is row equivalent to the matrix $I$ if $d-cb \neq 0$.

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