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