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Linear Algebra

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Moderate

Determinant of a Cyclic Permutation

LINALG-LWZTG9

If $\{\vec{e}_1,\dots,\vec{e}_n\}$ is the standard basis for $\mathbb{R}^n$ and $A$ is an $n\times n$ matrix such that:

$$\begin{align*} A\vec{e}_1&=\vec{e}_2\\\ A\vec{e}_2&=\vec{e}_3\\\ &\vdots\\\ A\vec{e}_n&=\vec{e}_1\\\ \end{align*}$$

...then $\det{(A)}=$

A

$0$ regardless of $n$.

B

$-1$ if $n$ is odd and $+1$ if $n$ is even.

C

$-1$ if $n$ is even and $+1$ if $n$ is odd.

D

$n$