Question

A square matrix \[A=[a_{ij}]_{n\times n}\] is symmetric when which condition holds?

Options

• \[A^T=A\]

• \[A+A^T=-A\]

• \[A-A^T=A\]

• \[A^T=-A\]

Answer 1

A symmetric matrix is defined by the equality \[A^T=A\]. Thus, transposing the matrix leaves every entry in the same position with the same value.