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Let A be an orthogonal matrix, and B is ...

Let A be an orthogonal matrix, and B is a matrix such that `AB=BA`, then show that `AB^(T)=B^(T)A`.

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Given `A A^(T)=I, AB=BA`
`:. (AB)^(T)=(BA)^(T)`
`implies B^(T) A^(T)=A^(T) B^(T)`
`implies B^(T) A^(T) A=A^(T) B^(T) A`
`implies B^(T)=A^(T) B^(T) A`
`implies AB^(T)=A A^(T) B^(T)A`
`implies AB^(T)=B^(T)A`
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