Answer
See below
Work Step by Step
a) If the volume of the parallelepiped is defined by the row vectors of the matrix $A$, then $|det(A)|$ can be used to find the volume of the parallelepiped.
$\det(A)=2+12k+36-4k-18-12\\
=8+8k\\
\rightarrow |\det(A)|=|8+8k|$
b) Since the volume determined columns of $A$ are the same as the volume determined rows of $A^T$, but the determinants of $A$ and $A^T$ are the same, the response from (a) remains unchanged. So there we have $|det (A)| = |det (A^T)|$
(c) The matrix $A$ is invertible if and only if $det (A)\ne 0$, according to Theorem 3.2.5. This is equivalent to $8+8k \ne 0 \rightarrow k\ne -1$ in this situation.
