Question

Prove that the diagonal elements of a skew symmetric matrix are all zeros.

Answer 1

Let A be a skew symmetric matrix, then:
A' = -A

Let X(i, j) denote the element at the ith row and jth column of the matrix X.

For diagonal elements, i = j = k (say).

For every element A(i, j),
A(j, i) = -A(i, j)
For diagonal elements, i = j = k.
A(k, k) = -A(k, k)
2A(k, k) = 0
A(k, k) = 0
:: all the diagonal elements of a skew symmetric matrix are zeroes.