Answer
$A$ is an invertible matrix.
(Th.8, (a) and (b))
Work Step by Step
(The exercise wants us to use technology)
Defining A in MATLAB (or, in my case a clone: OCTAVE GNU)
A=[4 0 -7 -7; -6 1 11 9;7 -5 10 19;-1 2 3 -1]
rref(A)
returns the $I_{4}$ matrix,
$\mathrm{b}. \quad A$ is row equivalent to the $n\times n$ identity matrix.
is valid. Then, by Th.8
$\mathrm{a}. \quad A$ is an invertible matrix.
is valid as well
$A$ is an invertible matrix.
(Th.8, (a) and (b))