Question

Linear Algebra: Show that if A is skew-symmetric, then A is a square matrix which has only zeros on its main diagonal.

Answer 1

A is skew-symmetric then its transpose= -A
a(ij) = - a(ji)
the limits of i and j must be the same => A has same number of columns and rows => it is a square matrix
for the diagonal
a(ii) = -a(ii)
which is only true for a(ii)=0