Answer
$A$ is an invertible matrix.
(Th8, (a) and (c))
Work Step by Step
We can see, without performing the actual row transformations, that
A has 3 pivot positions (on the diagonal).
So, looking at Th.8,
$\mathrm{c}.\quad A$ has $n$ pivot positions.
is valid. Then,
$\mathrm{a}. \quad A$ is an invertible matrix.
is valid as well
$A$ is an invertible matrix.
(Th8, (a) and (c))