Question

Consider the matrix $J_0=\left[\begin{array}{cccccc}0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 1& 0& 0& 0\\ 0& 1& 0& 0& 0& 0\\ 1& 0& 0& 0& 0& 0\end{array}\right]$ which is obtained by reversing the order of the columns of the identity matrix $I_0$.
Let $P=I_0+\alpha J_0$, where a is a non-negative real number. THe value of $\alpha$ for which $det\left(P\right)=0$

Answer 1

$\left|P\right|=\left[\begin{array}{cccccc}1& 0& 0& 0& 0& \alpha \\ 0& 1& 0& 0& \alpha & 0\\ 0& 0& 1& \alpha & 0& 0\\ 0& 0& \alpha & 1& 0& 0\\ 0& \alpha & 0& 0& 1& 0\\ \alpha & 0& 0& 0& 0& 1\end{array}\right]=0$ (given)
$1-{\alpha }^0=0$
${\alpha }^0=1,\alpha ϵR$
\Rightarrow $\alpha =\pm 1$
$\alpha$ is non-negative real number
\Rightarrow $\alpha =1$