Question

If the matrix A is both symmetric and skew-symmetric, show that A is a zero matrix.

Answer 1

Given that matrix A is both symmetric and skew symmetric, then,

We have A = A’ ……(i)

And A = -A’ ……(ii)

From (i) and (ii) we get,

A’ = -A’,

2A’ = 0

A’ = 0

Then, A = 0

Hence proved.