DeterminantByDef

例題次の行列式を求めよ．

$\displaystyle \left \vert \begin{array}{ccccc} 0&0&0&1&0\\ 0&1&0&0&0\\ 0&0&0&0&1\\ 1&0&0&0&0\\ 0&0&1&0&0 \end{array}\right\vert$

解答

	$\displaystyle {}$	$\displaystyle \left\vert\begin{array}{rrrrr} 0&0&0&1&0\\ 0&1&0&0&0\\ 0&0&0&0&1\\ 1&0&0&0&0\\ 0&0&1&0&0 \end{array}\right\vert$
	$\displaystyle =$	$\displaystyle {\rm sgn}(4,2,5,1,3)1\cdot 1\cdot 1\cdot 1 \cdot 1 = - sgn(1,2,5,4,3) = sgn(1,2,3,4,5) = +1$