Question

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

Answer 1

Let A be a skew - symmetric matrix. then by definition A' =-A or the (i,j) th element of A' = The (i,j) th element of A

For the diagonal elements i = j or the (i,j) the element of A =- the (i,j) th element of A or the (i,i) th element of A =0

Hence the diagonal elements are all zero.