Let A be a skew-symmetric matrix of odd order, then $\left|A\right|$ is equal to

Solution:

Let $A$ be a skew-symmetric matrix of odd order $(2 n + l)$say. Since $A$ is skew-symmetric.

   $\begin{array}{l}\therefore A^T=-A\\ \Rightarrow \left|A^T\right|=|-A|\\ \Rightarrow \left|A^T\right|=(-1{)}^{2n+1}|A|\\ \Rightarrow \left|A^T\right|=-\left|A\right|\\ \Rightarrow \left|A\right|=-\left|A\right|\Rightarrow 2\left|A\right|=0\Rightarrow \left|A\right|=0\end{array}$