Hoffman Kunze, reasonable name for the scalar c with $\det A = c$ I am working on problem 5.3.11 of Kunze.
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Let $T$ be a linear operator on $F^n$. Define
$D_T(\alpha_1, \alpha_2, ..., \alpha_n) = \det(T\alpha_1, T\alpha_2,
 ..., T\alpha_n) $
(a) Show that $D_T$ is an alternating $n$-linear function.
(b) If
$c = \det(T\epsilon_1, T\epsilon_2, ..., T\epsilon_n)$
show that for any $n$ vectors $\alpha_1, \alpha_2, ..., \alpha_n$ we
have
$\det(T\alpha_1, T\alpha_2, ..., T\alpha_n) = c\det(\alpha_1, \alpha_2,
 ..., \alpha_n)$
(c) if $B$ is any ordered basis for $F^n$ and $A$ is the matrix of $T$
in the ordered basis $B$, show that $\det A=c$
(d) What do you think is a reasonable name for the scalar $c$?

Here, I've done up to (c) and showed the important part but I can't think of a suitable name for scalar $c$. And I couldn't find hints regarding this either. Can you help me figure out? If this $c$ indeed has a famous name, a mere name would help a lot, since I have no idea what to search for.

You are overthinking it. I believe he simply meant that it's appropriate to define the determinant of a linear operator $T$ by $\det T\stackrel{\text{def}}{=}c$.
