Question

For a skew-symmetric matrix \[A=[a_{ij}]_{n\times n}\], which relation holds for all \[i\] and \[j\]?

Options

• \[a_{ij}=a_{ji}\]

• \[a_{ij}=-a_{ji}\]

• \[a_{ij}=-a_{ii}\]

• \[a_{ij}=a_{ii}\]

Answer 1

The equation \[A^T=-A\] gives the entrywise relation \[a_{ij}=-a_{ji}\]. Therefore, entries on opposite sides of the main diagonal have opposite signs.