Question

Which identity is used to replace \[(A^T)^T\] by \[A\] when proving that \[A+A^T\] is symmetric?

Options

• \[(A+A^T)^T=-A\]

• \[(A^T)^T=A\]

• \[(A^T)^T=-A\]

• \[(A-A^T)^T=A\]

Answer 1

Taking the transpose twice returns the original matrix. Hence \[(A^T)^T=A\], which allows \[A^T+(A^T)^T\] to become \[A^T+A\].