More Problems on Linear Systems and Matrices

Problem. Let $A$ and $I_2$ be the matrices

\begin{displaymath}A = \left(\begin{array}{ll}
a & b \\
c & d
\end{array} \r...
...eft(\begin{array}{ll}
1 & 0 \\
0 & 1
\end{array} \right)\;.\end{displaymath}

Show that if $ad -bc \neq 0$ then $A$ and $I_2$ are row equivalent.
Recall that two matrices are row equivalent iff one may be obtained from the other one via row elementary operations.

Answer.

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