A matrix A is said to be skew symmetric if A^T = -A. Show that is a matrix is skew symmetric then its diagonal entries must all be 0.

Question

A^T meant to be A transpose.

Answer 1

Let a(i,j) stand for the element of A on the ith row and jth column.

Let
A be a skew symmetric matrix.

By the definition of skew-symmetry,
a(j,i)=-a(i,j)

On the diagonal,
i=j
=> a(i,i)=-a(i,i)
=> a(i,i)=0

since x=-x => x=0