Question

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

Options

• \[a_{ij}=-a_{ii}\]

• \[a_{ij}=-a_{ji}\]

• \[a_{ij}=0\]

• \[a_{ij}=a_{ji}\]

Answer 1

The condition \[A^T=A\] means that an entry and its reflected entry across the main diagonal are equal. Hence \[a_{ij}=a_{ji}\] for all \[i\] and \[j\].