Question

Which transpose property justifies the step \[(A+A^T)^T=A^T+(A^T)^T\]?

विकल्प

• \[(A-B)^T=A^T+B^T\]

• \[(A+B)^T=A^T+B^T\]

• \[(A^T)^T=-A\]

• \[(AB)^T=A^TB^T\]

Answer 1

The transpose distributes over addition: \[(A+B)^T=A^T+B^T\]. Applying this with \[B=A^T\] produces \[A^T+(A^T)^T\].