Find Sum of All Elements of a Skew-Symmetric Matrix

Given:

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

Property Used:

\[ a_{ij} = -a_{ji} \]

Step 1: Pair Elements

\[ a_{ij} + a_{ji} = 0 \]

Step 2: Diagonal Elements

\[ a_{ii} = 0 \]

Step 3: Total Sum

\[ \sum_i \sum_j a_{ij} = 0 \]

Final Answer:

\[ \boxed{0} \]

All elements cancel in pairs, so total sum is zero.