Question

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

Answer 1

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

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

Now,

${\left(kA\right)}^T$

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

$=k\left(-A\right)$ [Using (1)]

$=-kA$

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

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