Department of Mathematics, K.T.H.M. College, Nashik

Q.(NET Dec 2014)
The Determinant of \(n \times n \) permutation matrix is
\[ \begin{pmatrix} 0 & 0 & \cdots & 1 \\ 0  & 0 & 1 & 0  \\ \vdots & \vdots & \ddots & \vdots \\ 1 & 0 & \cdots & 0\end{pmatrix} \]
A) \( (-1)^n  \)
B) \(  (-1)^{\frac{n}{2}} \)
C) \(  -1 \)
D) \(  1 \)

Ans . \(\textbf{Option C}\)
Option C: The determinant of backward identity matrix is \(  -1 \).