Answer
No.
Work Step by Step
If two columns of A are identical, then the statement
$\mathrm{e}.\quad $ The columns of $A$ form a linearly independent set.
of Th.8 is false.
Then, the statement
$\mathrm{a}. \quad A$ is an invertible matrix.
is also false , because Th.8 lists equivalent statements.
Therefore,
No, a square matrix with identical columns can not be invertible.
