Answer
$A$ is not an invertible matrix.
(Th.8, (a) and (b))
Work Step by Step
Adding $3R_{1}$ to $R_{3}$
$A\sim\left[\begin{array}{lll}
1 & -5 & -4\\
0 & 3 & 4\\
0 & -9 & -12
\end{array}\right] $adding $3R_{2}$ to $R_{3}$
$\sim\left[\begin{array}{lll}
1 & -5 & -4\\
0 & 3 & 4\\
0 & 0 & 0
\end{array}\right]$
we see that $A$ can not row-reduce to $I_{3}$
So, looking at Th.8,
$\mathrm{b}. \quad A$ is row equivalent to the $n\times n$ identity matrix..
is not valid. Then,
$\mathrm{a}. \quad A$ is an invertible matrix.
is not valid as well
$A$ is not an invertible matrix.
(Th.8, (a) and (b))