Question

The elements on the main diagonal of a skew-symmetric matrix are all ...........

Answer 1

Let $A=\left[a_{ij}\right]$ be a skew-symmetric matrix. Then, $a_{ij}=-a_{ji}$ for all i, j (by definition). Hence,
$a_{ii}=-a_{ii}$ for all values of i
$\Rightarrow 2a_{ii}=0$
$\Rightarrow a_{ii}=0$ for all values of i
$\Rightarrow a_{11}=a_{22}=a_{33}=.........=a_{nn}=0$