If A is a skew-symmetric matrix,

It is given that, $A$ is a skew-symmetric matrix.

$\therefore A^{T}=-A$               ...(1)

Now,

$(k A)^{T}$

$=k\left(A^{T}\right)$

$=k(-A)$              [Using (1)]

$=-k A$

Since $(k A)^{T}=-k A$, so the matrix $k A$ ( $k$ is any scalar) is a skew-symmetric matrix.

If $A$ is a skew-symmetric matrix, then $k A$ is a ( $k$ is any scalar).