Question

Let $A$ be a square matrix, then prove that $A-A^T$ is a skew-symmetric matrix.

Answer 1

Given $A$ be a square matrix.

Let, $B=A-A^T$.

Now,

$B^T$$=A^T-(A^T{)}^T$

$=A^T-A$

$=-(A-A^T)$

$=-B$.

As $B^T=-B$ then $B$ i.e. $A-A^T$ is a skew-symmetric matrix.