Answer
This is so because of Th.8.(a and e), and the fact that
if $A$ is invertible, then its inverse $A^{-1}$ is invertible as well.
Work Step by Step
If $A$ is invertible, then its inverse $A^{-1}$ is invertible as well.
Theorem 8 lists equivalent statements. Among them are:
$\mathrm{a}. \quad A$ is an invertible matrix.
and
$\mathrm{e}.\quad $ The columns of $A$ form a linearly independent set.
Substitute $A$ with $A^{-1}$ in the above statements.
If (a) is true, then so is (e)