If a matrix P is both symmetric and skew-symmetric, then

The correct answer is Option (3) → P is a zero matrix

Given: P is both symmetric and skew-symmetric.

$Symmetric: P^T = P$

$Skew-symmetric: P^T = -P$

$Equating: P = -P \Rightarrow 2P = 0 \Rightarrow P = 0$

Hence, P is a zero matrix.