Show that the elements along the main diagonal of a skew symmetric matrix are all zero.

Pls. answer

For a skew symmetric matrix A

A^T + A = 0

Therefore

A^T = -A---------eq.1

We know

Diagonal elements of A =  Diagonal elements of A^T ------eq.2

Now from eq.1 and eq.2

Diaganol elements of A and Diagonal elements of AT should be equal as well as of opposite  signs

This is possible only when all diagonal elements are 0

Hence Proved.