If the matrix A is both symmetric and skew symmetric, then

Question

Philoid · Accepted Answer

Given A is both symmetric and skew symmetric matrix then, A = A’ and also A = -A’

⇒ A’ = -A’

⇒ 2A’ = 0

⇒ A’ = O

Clearly it is observed that transpose of A is a null matrix or zero matrix then matrix A must also be a zero matrix.

Hence A is a zero matrix.