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Question
Which transpose property justifies the step \[(A+A^T)^T=A^T+(A^T)^T\]?
Options
\[(A-B)^T=A^T+B^T\]
\[(A+B)^T=A^T+B^T\]
\[(A^T)^T=-A\]
\[(AB)^T=A^TB^T\]
MCQ
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Solution
The transpose distributes over addition: \[(A+B)^T=A^T+B^T\]. Applying this with \[B=A^T\] produces \[A^T+(A^T)^T\].
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