Answer
A is not invertible
Work Step by Step
If we don't want many calculations, we test a criterion from Th.8:
$\mathrm{e}.\quad $ The columns of $A$ form a linearly independent set.
(then: $\mathrm{a}. \quad A$ is an invertible matrix.)
$6= -4\displaystyle \times(-\frac{3}{2})$ , and $-9=6\displaystyle \times\frac{7}{5}$,
so the columns are t multiples, meaning they are linearly dependent.
A is not invertible
Another test for 2$\times$2 matrices is testing $ad-bc.$
$(-4)(-9)-(6)(6)=0$ , so A is not invertible
