Find Sum of Diagonal Elements of a Skew-Symmetric Matrix

Given:

\[ A = [a_{ij}] \text{ is skew-symmetric} \]

Property Used:

\[ A^T = -A \Rightarrow a_{ij} = -a_{ji} \]

Step 1: Consider Diagonal Elements

\[ a_{ii} = -a_{ii} \]

Step 2: Solve

\[ 2a_{ii} = 0 \Rightarrow a_{ii} = 0 \]

Step 3: Sum of Diagonal Elements

\[ \sum_i a_{ii} = 0 \]

Final Answer:

\[ \boxed{0} \]

All diagonal elements of a skew-symmetric matrix are zero.