Question

The sum of two skew-symmetric matrices is always __________ matrix.

Answer 1

Let A and B be two skew-symmetric matrices.

∴ A^T = −A and B^T = −B .....(1)

Now,

${\left(A+B\right)}^T$

$=A^T+B^T$

$=-A-B$ [From (1)]

$=-\left(A+B\right)$

$\therefore {\left(A+B\right)}^T=-\left(A+B\right)$

Thus, the sum of two skew-symmetric matrices is always skew-symmetric matrix.

The sum of two skew-symmetric matrices is always __skew-symmetric__ matrix.