Let A be a skew-symmetric matrix of odd order, then A is equal to

Solution:

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

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

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