Question

If \[C=A-A^T\] for a square matrix \[A\], what is \[C^T\]?

Options

• \[C^T=A+A^T\]

• \[C^T=C\]

• \[C^T=-C\]

• \[C^T=0\]

Answer 1

Using the transpose rule for subtraction, \[C^T=(A-A^T)^T=A^T-A\]. Since \[A^T-A=-(A-A^T)\], it follows that \[C^T=-C\].